dly help me with this issue. Um, Yeah, I uh, as mentioned our support team is basically ready to answer your inquiries So, um, just give it some time our support team is basically working on other tickets as well So once they come across your ticket, they'll be able to answer it. You'll be assisted. All right Okay from detroit. Do you have to be in the philippines or can you Be a support agent from elsewhere. We have uh, we have our support team as well from other countries We have spanish, portuguese We have thai. So let me um, yeah, I believe that's it Okay, give me a quick sec. Just give me a quick sec. I'm actually asking some of the support team for all The support, uh Support agents that we have for other countries Um, don't know it on top of my head. So I mean mainly it's spanish portuguese thai hindi I believe we have russian And uh, what else Chinese I mean, we are still uh, we're still we're still small. So basically we are looking into maybe having some german support vietnamese What else? Yeah, basically those are the frequent ones that I see that are basically, um That are you know having a large Large audience for youtube. Also, we have dutch. So we have chinese dutch english hindi spanish portuguese and Russian and thai support. So we have eight after the moment. We're looking to add more So that we can expand our Spend our revisions as well Expand the youtube community so we can grow together Okay, but if ever you would like to work for freedom Well, we or that was one of the first things that we had of that interested that interest some of the viewers Let me provide you a link This is basically our support link for job openings here at freedom So maybe you maybe if you can get accepted with freedom can come here in hq work with us So just check the link out. All right Okay from andro punk I had requested a month ago for partnership, but they declined it for no reason saying I had cow I had copyright content, but I had I had but it was long gone. Maybe you can do a re-review of your channel. So you can contact our support team advice them that You will be requesting for a another review of your channel Make sure to delete all copyright content and spam content. Make sure your channel is in good standing as well. Okay Okay from travis whitford when will freedom start inviting people again because I've been waiting for a while. Well, um, as mentioned we are having some system updates. That's why We are like we are unable to send out the invites We are making sure that once we send out the invites you would be receiving it and um We appreciate your patience about this once we are ready to send out the invite Please make sure to have your contact information updated via your skype via your email address in your freedom dashboard Because we will be contacting everyone is on our repenting list to be invited to join freedom. Okay Okay, andro punk. I did that too, but they declined it as well. No issues Hmm That's odd because uh, whenever uh, there is basically a decline of application We will be telling you the reason why so Maybe you can go ahead and check your channel. I believe you will be provided links if uh, if our quality control team found out Uh, some copyright content on your channel We are actually providing you links on how what or on how copyright works How fair use is working? So once you're done with the links try to apply that to your channel. Okay Okay, uh, we have a suggestion here from game form stars and with freedom and I love it How can I help but I can't work though because I have disabilities like Like uh, sorry, let me rephrase, uh, but I can't work though because I have disabilities Like can I do a show similar to the george show? I just want to help Okay, well, um that I mean that can be worked upon if you can, uh, maybe Um, yeah, just check the job openings that we have here in freedom and um if they can find potential of you, uh You know making videos just like george, maybe we can work things out for arrangements Okay from gargs gaming. Does george also do live streams? Well, I haven't Really noticed it but as far as I can remember anthony did one before And I believe I'm the second one. So I don't think he is but I believe he will be doing one in the near future Just a hunch, right? So um caught up with your questions guys any other questions that you can do Um, well, I was just informed by my other colleagues that actually george is doing some live streams Before so or sometimes so it's really not that frequent, but maybe we can uh You can ask him to do one We're in the near future Yeah, maybe that's a good idea, right? So yeah guys, um Yeah, again, I just want to thank you personally for tuning in I know it's basically a different time zone in you guys Some of you guys are still awake So or I mean in the case of others it's already early early morning. So Um, yeah, we I do appreciate you tuning in and we thank you for Supporting freedom. Let me just drink some water here my freedom mug. There you go So we are waiting for some questions here guys Yeah, guys, no no further questions. Just like a school just like a school setup So again, yeah, let me again show you our websites. Give me a quick sec There you go. Here's our freedom website www.freedom.tm And we also have our support page support.tm And open the ticket here once you click on this one ask the community you will be routed to this website www.community.tm This is our community forums And if you want to do a live chat with other freedom partners and with the freedom community There's our discord server The links are basically provided in the video descriptions of every video in freedom central And as well as i'm providing the links as well. Ashley is back. She is providing as well links for the community team and as well as the discord servers Garg's Gaming does freedom send gift to their partners? Well, sometimes. Yeah, I believe there was a time I believe in christmas. We have sent out freedom shirts so Yeah, there's a possibility that we'll be doing it again, but i'm not sure When we'll be doing that so just stay tuned. Okay All right, we have a shanti bacon online. She's one of our Our viewers from yesterday's stream. How are you? Hey, how's it going? I'm just fine. How are you doing? We started early so Yeah Game form stars. Good night guys. See you tomorrow chico. Would you stream tomorrow? Yes? I will do a stream again. So i'm expecting you to be here tomorrow as well Um, I think i'm gonna be starting at the same time 10 a.m. Manila, but i'm not sure yet But uh, yeah, just uh keep tuned in to this live stream And we can have a good conversation here. So good night. Okay Okay, garg's gaming the stream is getting bored Can you show me the minecraft server gameplay? Well, I don't play minecraft. Let me check if I have that here Let me see. Let me see if I can Send you the link for the minecraft video I'm unable to find that but uh, I'll get back to you in a moment when I find that That minecraft gameplay. All right Oh shanti bacon. I'm a he everybody thinks i'm a girl. Well, I'm sorry about that I mean i'm taken by your name a shanti. So Yeah, I think it's like a girl name, but I'm sorry if I'm calling you a girl, but Uh, sir, welcome to the live stream and uh, yeah, every uh, I hope you are enjoying your stay here Okay, garg's gaming. Is anyone else with you? Me i'm actually a solo flight right now, but we are looking into other Other like other freedom Freedom agents or freedom support agents to be here as well And uh speaking of which I have my first companion. No, actually not my first companion. I have your stuff Hello I have your stuff and I'm gonna be doing more things. He's gonna be doing more things as well. So Let's me borrow your chair. Yeah. Um, yep, maybe step will take over for a quick moment. All right. Are you taking a break? I'm taking a break guys. I've come to dive under the table and look for usb slots again I will be back in a second USB slots Sorry about that guys Chico is taking a little break and I'm gonna put more new graphics and stuff up that we've been working on So let's see what they look like Okay, let me see So first we need to remove the background that we have And then we need to bring this clip in And then we're gonna make this all big and lovely Then we're gonna move it to the bottom layer And we're gonna get rid of that Um, what do you think I think the chroma key needs a bit of work, which we'll get around to tomorrow But I think that looks pretty nice What do you guys think let me know You guys want to see a few things in dashboard? Well, I can certainly do that I can show you some of the products I work on inside dashboard while Chico's having his break Give me a second. Let me get logged in. I want to be logged in on that one Oh, I need to turn that element off as well. I missed an element Silly bee Where is it that one Yeah Okay, that that one's been messed up. We're gonna leave that element off for now There's a bit of an issue with that one Because it's double layering because I forgot to expand it to the whole link for the video because I'm a dumb dumb Yep, so I will fix the social media icons later So while I'm here, let's have a quick look through dashboard. I guess No, worry. We're gonna improve the chroma key and as we go along I know it's not particularly clean at the minute. We've got a few bits of light into play. We've got some new lights I'm gonna mess with all that sort of stuff. So this is as Mr George puts it the shiny freedom dashboard and we should be using this as partner. So you don't see secret things Oh, excuse me a minute while I sneeze Okay, it was one of those fake sneezes Well, we all hate those. Anyway, let's have a quick look through what we've got going on it So one of the projects I personally work on is game giveaways, which you'll find here This is sort of my baby. I designed the system I worked out all the deals that for the games we've got and as you can see we've got quite a few in here now Why is it still? No, it's fine So this is where you guys can pick up some free video games free software or that kind of thing So like let's have a look at this one. Why is that on that admin view still? It's supposed to be As a partner. Okay, that didn't work. I'm gonna switch scene again Okay, I can't show you that one guys. I'm afraid Unless I can sign into my personal account from here. Let's see Because I can't show you all the admin trickery I just can't it's just not done Uh an account let's have my personal one Because I don't mind you guys seeing my account details because I don't use it very often anyway Because this is an old and dead channel Okay, let me just get logged in here We're gonna jump on this account We're gonna jump on there Okay, one thing guys is just log in. Hello Ashante bacon Bacon is good Of course, you don't want to leave LW 001 Nobody wants to leave Anyway, we are now in the dashboard on my personal account So let's have a little look through and see what we've got going here So one of the projects I work on is game giveaway. So this was a project that started out What a year and a half ago and was very rushed and then once I came on board with freedom I reconcepted everything I redesigned the system entirely And we have what you see today. So the way this works is there's three different tiers of games for different subscriber ranges So if you guys Are smaller youtubers you can get access to everything within this section So say I wanted for instance of free copy of creepy castle I would keep click on creepy castle I can click here to generate a key which i'm not going to do because I don't want to steal a key from you guys I can check out the trailer there Trailer's down apparently so don't worry about that We've got a little bit of a description here And then the most crucial thing you guys need to do is as soon as you guys have made a video about the game Come back and submit it. This is because if you claim three Keys That's if you claim three keys and don't submit a video you will be locked out of the system So you guys need to make sure that when you're claiming keys from this thing you always submit videos And that also allows us to go to other companies say We got a thousand videos back for this video game. So What about your game give us a load of copies of your game? We'll throw them in our dashboard system. You'll get a load of free promotion But we can only do that with your guys help and this is where we run into some issues occasionally We need your guys help so we can grow the network and make things even better You help us we help you. It's the way family works So let's see what else we've got in here in a minute So creepy castle is an awesome little game. You should all keep check out It'll do two is actually one of my favorite games we've had on here It's Like the art style is just amazing. Let me pull up the trailer for it'll do two and show you guys What it what exactly it is We should probably type in trailer So this is the it'll do two announcement trailer Let's throw it on there. Let's make it full screen for you guys. So the art style of this game I Absolutely adore. It's absolutely I know it's it's just one of those things that really appeals to me and I've moved over a little bit to the branding Isn't hopefully blocking my face as much But yeah, I really love the art style of this game and it is a true sort of adventuring dungeon crawly explorer uh, it's RPG-ish there's lots of items there's lots of different bosses as you can see And it really is an amazing game. So this is definitely something that you guys should jump on game giveaways and grab So let's see what else we've got in the dashboard for you guys So also in the dashboard we have lots and lots of music for you So you guys should all as freedom partners be pretty familiar with things like position music So position music is a massive massive music library. We provide to you guys Where you will find literally Thousands of free music tracks. So let's go on position music and see what it has to offer So I'll just open up the position music website and we'll have a quick flick through a couple of tracks and see what we think Uh, yeah, I um let chico go for a quick break while I put put in some new graphics and stuff like that And I just thought I'd talk to you guys for five minutes Uh while he does his thing So I'm just loading up position music now and we'll have a look at a few of the tracks on here So one of the things that a lot of you guys don't realize about position music is that this Literally is world-class music. This is in movies. This is in video games This is in some of the biggest things that are released media-wise So for instance, one of the things that's just been shown is uh titanfall 2, which I'm sure a lot of you are familiar with So titanfall 2 actually the trailer music, which I'm going to show you guys now Is a music from position music. Yes. That's the same music library. You guys have got access to So if you hear the background track here then this is Literally the same sort of music you guys have access to so AAA video game developers are using a music library You have access to because that's how good this stuff is when people say the music is very good that we provide There couldn't be more wrong if it's good enough for titanfall. It's been featured in the transformers movies Is in an upcoming mute movie called chips That's going to be huge is featured in so much like triple a hollywood level stuff And then we get to people turn around say well the music's not very good. There's I think over 20,000 tracks you guys have got access to for free So if you guys can't really find a track in here, you like then I don't know whether it's the size fault or not So it's also a bit of movies like magnificent magnificent seven. Let's take a quick look at that. Let me just open this up So this is the trailer for Magnificent seven and again the music and sound effects and things like that It all comes from position music, which is a library. You guys have got access to for free We got to do that for free tends to use so check out position music Just have a look through Your freedom dashboard and you'll see it in there. Grab yourself some triple a hollywood music So let's see what Chico is away Because I am a product man. I like working on all our fancy products and then sharing them with you guys So it makes sense that I talk about them a little bit So let's have a look at the play now links So play now is something we used to do a very long time ago and we are now doing again So I don't know whether any of you guys are familiar with play now. So let's have a quick look at it. So Let's first check out wt fast Okay, switching over so wt fast is uh, basically a software system that's designed to reduce your lag in video games So with the play now links you could essentially Personalize get your personalized play now link You can put this in your video description And you can generate some revenue using this and now the revenue varies from product to product Well, it's as simple as that make a quick wt fast review and then throw that in your description And maybe you'll make a few books from that Then we have a tri-dev smart cam which is an awesome little piece of software So what you can see here is it can be used Essentially as a replacement for a green screen So we can use it to blur out backgrounds We can use it to replace backgrounds and we can use it to make your background transparent Which is absolutely amazing. I've used this software personally myself And I must say it's one of the most amazing pieces of software I've ever used if you've got a static background So again, this is something you can download the trial of uh make a video on it And then get your personalized play now link Put it in the description and see if some people are interested in it I remind you of jacksepticeye. I'm not irish sir. I'm actually very very english Anyway, let's have a look at some more products exploit you're all familiar with It's what I'm using to stream to you guys right now So again personalized play now link use the exploit trial make a video review throw this in the description And you'll make a few dollars if people like it And then we come on to my favorite bit video games Because I am a pretty huge video game Nerd so be you guys might have seen the fallout livestream We did a few months ago and stuff like that where I spent like 20 hours playing fallout on stream or something So let's have a quick look at what we've got here. So this section of Played out is dedicated to video games. So we've got star wars the old republic in here This is actually a video game that I played a ton back when it was released It's spy So if any of you get any of you familiar with games like mass effect I've been advised to do by you guys maybe by the same company and it uses the same story and conversation system It's got I think it's got which is what i'm gonna I want to say 10 classes now. I haven't played for a while. So I may be wrong Let's see if we can find a quick cutscene. So it's got the traditional speech wheel Can you stop talking please? Why do you want me to stop talking? What a guy I'm gonna continue because this is my show So yeah, this is star wars the old republic made by by aware that was the conversation system that you see in Mass Effect you see in dragon age And it's in an mmo, which is pretty impressive. What else we got on it Warframe warframe is a game again that I played a little bit of I've actually played this on a ps4 And oh, sorry the video was played. That's my bad Um, I'll make sure that's not happening for the rest of these So, uh, yeah, what was I saying warframe is a game. I uh played a little bit on PS4 and because I couldn't get used to the Controls of the ps4. I couldn't really get into it Yep, I'm gonna try not to play any more videos. That is my bad. Let me just check the mixer Yeah, there should be no background audio now So, yeah, this this is a game I played a little bit of and Got a little bit fed up of honestly on ps4 But again, if it's your sort of game because I know tons of people that love this game Make a video on it Grab your play now link thrown in the description And hopefully if some of your fans come and play the game with you and sign up using your link You'll make a little bit of extra money Um, thank you very much for coming LW 001 No, I cannot stop talking sir Thank you very much for coming and I hope you have a wonderful day at school So then we have League of Legends everyone familiar with League of Legends It's a very very normal game that we've all seen at millions and millions of videos on So I'm not going to go too much into that one World of tanks, let me just make sure I'm muted that video. Yeah, I did turn that video off World of tanks world of tanks is a big game where you drive big tanks and you blow up other people's tanks It's a very pvp focused game And now there's world warships world of war planes as all sorts of military base games made by this studio So again, if if you like it make a couple of videos on it grab your play now link Invite your audience to play with you ask them to sign up using the link in your video description And you'll make a few books Oh, this is one of those games that I got addicted to this is called a terror online It's a massively multiplayer online game, but it's a little bit different to most So this game is based on action combat So what I mean by that is instead of you standing there and tab targeting and hitting One one one one one two three nine seven two nine seven and doing a basic rotation like in games of world of warcraft movement positioning And avoiding things is super super important in this game until you've played it. You don't even know Like this was one of my favorite mmo's ever Zimrick this money is just paid straight into your paper account once it's been processed So for your play now links in your descriptions once payments have been processed It will be sent to your payback link. You can make a little bit bonus cash So yeah terror online if you guys haven't checked her online online now I highly highly recommend it. This was One of my favorite mmo's for a long time the main reason I dropped terror online was because I moved to the Philippines So my time time zone was off from my friends. So I couldn't really play with them anymore But otherwise I'd probably still be playing this now. This was one of my favorite mmo's for a long time Um the play now links do have country Restrictions and things of that nature. So uh, if you're in certain countries, they might not work It's different for every single game Uh, then we have war thunder Uh, I thought it's a little bit about that when we was talking about world of tanks. It's a aeroplane game It's a pvp game. You blow people out of the sky Cloud pirates, this is one. I'm not actually familiar with most other games on here. I'm familiar with so I can't tell you a lot Let's just read the description Deck out your pirate airship with cutting edge weaponry in cloud cloud pirates An action mmo in which you fire your cannons to crush your enemies in fast-paced aerial battles Okay, that sounds kind of cool actually. I might have to have a look at This game take command of your very own airship and navigate the clouds to battle rival captains in exciting team combat What do you think the uh voice am I hitting sort of the pirate theme or do I just sound silly? So yeah, this sounds like another pvp mmo in where you can customize your very own Pirate airship and fight in the clouds. That sounds pretty cool Uh, again, if you want to play now link, you just click the personalized play now link button And copy and paste this into your description into relevant videos So make sure it's a video about this game or you will get in trouble and not be able to use the system anymore Then we have neverwinter another online mmo Uh pirate hat and an eye patch. I'll see what I can do for next time Neverwinter is another mmo. They tried to do the action-based combat system Didn't quite do it as well as terror, but I do love in neverwinter that it's an It's it's a little bit More Sort of time friendly So instead of large raids and raids that take Hours and hours and hours neverwinters more broken down in sort of the maximum group size is five rather than the traditional 24 or 20 So it's a little bit easy to group up and do stuff in neverwinter So definitely check never neverwinter out Then we have big farm which i'm not sure what this is We're gonna move on And then we have world of warships again made by the same company that do world of tanks and world of planes So grab your personalised play now link from here and see what you can do with it Zimmerich says I play for honor and can't seem to get noticed Is there any way that freedom can help me with that? Yeah, so as lw001 says good tags are essential to getting noticed As well as that some other ways you can influence your metadata is to make sure the start of your description is around about 300 word blog post So the description does count Do not spam your description with links because that will get you banned from youtube But try and make the first sort of 300 words of your description a nicely formatted description of what's going on in the video Also, there's a lot of tag generators online that you can check out. So definitely check some of those out for better tag suggestions Make sure your thumbnails are super appealing and remember that they will look different on mobile and mobile is a massive audience on youtube now But anyway guys It looks like wrong shoulder.  He's got a nice new shiny background now So let's see what he can do with it Are you sure you got a new background you got a new background All right That's good. Thank you Steph Thank you so much Steph for the background All right There we go. It's basically the freedom.tm background. So yep, that's very good See here. Yeah, there you go Partner with support freedom. Yep. I can blend in with my black shirt with my freedom All right. So basically we are back We have a few hours left or we maybe have a one we have one hour left before 6 p.m here in manila. So Hit me up with your questions guys and um Let's get right to it All right from zimrackomg. I can see my comments awesome. Yep. Steph was the one who actually made that I would need to um Need to check. How did he do that? I believe he made sure he's using xplit so Yeah, there is an option here in xplit. So you can see um Can see the views or you can see the comments on your on the live chat Okay, so I believe Steph provided you with um With some insights about game giveaways So it's a good thing because he's the one handling that so if ever you have concerns about get games He's the guy so Alan, let's play you're still live. Yes. I am still live So yeah, I am Steph just uh fixed something in the um Fixed something in the background the lighting and um That should be good Okay, so um, how are you guys finding the new background? Is it good? Is it much better compared to um The the black freedom logo So, yeah, just uh hit us up in the chat section So that we can uh make it compare your comments and suggestions Okay, let's see here Okay, xle mc. Do I need to give information about my channel to join? Well, basically the the information that you would be providing is your youtube channel link You just need to make sure that your channel is linked in your freedom dashboard so that we can access your channel So that we can check and review your channel contents From zimrick do collabs or collaborations actually help. Yes, it does help. So let's say for example, um I'm a gamer. I need some uh, we need some Uh tutorials about let's say clash royale and let's say, um zimrick is basically an expert in clash royale And he's looking for let's say a practice battle and then i'm interested because um with um, you know I'm playing the same game you can do collaborations. We can make separate videos You can credit each other for the ideas and for the suggestions That will basically improve your content, right? Okay, from uh, we have a question from bruno max arm bruised What do I get with royalty free or with what do I get with royalty videos? Basically for royalty videos, you'd be able to use videos I mean royalty royalty free is basically no copyright videos So you'll be able to use these videos in your uh, your channel you can you can let's say Um, you can create news you can create. Um commentary about that specific video And once you are partnered with freedom You would have access to that and you should be able to see all the available videos that we have Let me show you some here Let's see Okay, let me just show you my screen real quick. Let me just load it up There you go. So basically, uh, you would be going here royalty free videos And you will see here some of the videos that we have that you can use On your channel. So you have viral videos. You have sports We have showbiz innovations, tourism, so you say the same news Right, right Reuters business and world news and also, um From Reuters, you just need to edit that and if ever you have other concerns you can check our FAQs and royalty royalty free tab Uh, let me just pull this up for you real quick. Give me a quick sec Uh, let me see here. Let me just pull up the tab here. Okay, let's see Oh, I think I put in the wrong one. Let me just check. Give me a moment Okay, let's see here. Right. Sorry for that. Uh, for that delay. Let me just check. Okay. All right Well, I'm sorry about that. You just need, um, I'm sorry for the misinformation You just need to go to your dashboard and see there five tabs free videos My favorites my downloads statistics and FAQ If you do have concerns, basically just click on this one. You should be able to check Uh, your royalty free videos. All right Any questions about, uh, the royalty free videos? Just click on this one FAQs. Let's see Okay, from Zimrick. What happens if I make videos about freedom? Well, just make sure that you are making A positive videos about freedom or I mean if you have commentaries you, um, if you Basically just make sure that you're not putting freedom in a negative light. So, um I mean it's free for you to create any videos that you would like as long as Uh, you would be abiding with youtube's policies regarding uploading videos If ever you would be reviewing a product or let's say you're reviewing freedom Just make sure it's pure commentary and pure criticism and not really Putting it on the negative light. All right for XLEMC How long do you guys Uh review a channel? So we are just having some system updates as of right now So, uh, we do appreciate your patience and we are sorry for the delay Once we are once our systems are up and running again, we will go ahead and send you Um, the invites and just make sure your contact information is updated Like your email address on your skype because there's a possibility that we can contact you via skype as well Okay, so, um, if you can see, um Let's see here Yeah, basically George Um CEO and founder of freedom basically had a message from me Hi Chico, that was a long pause without any speaking. I suggest always be talking even if it's small talk So George, thank you so much for the suggestion. I apologize. I was just about to check on that video So, um, yeah, I'll make sure to Um, I'll make sure to no no dead air and as well He said I also suggest increasing the microphone volume or speak louder as it feels at a little low in volume Hmm Not sure how to adjust this one, but thank you so much George For the suggestion, I'll make sure I'll apply this Um, moving forward and for tomorrow and for the next day's live stream. All right. Thanks so much And let's see See here, um, how can I support the freedom to channel me? Are you referring to have your channel be, um, updated or I mean Are you referring to your channel being partnered with freedom? So, uh, please try to clarify And let's see here From Monday night mystery, I have serious business with you guys. Please give me your skype If you have a like a like a business proposal Um, Monday night mystery, you can always email our support team www.support.tm Or you can email us directly at support at freedom.tm Please make sure if you will be provide if you would be presenting a business proposal make sure to provide everything Like the business proposal itself the goals Um, what you are actually looking for so that we can have this forwarded to the proper department. All right. All right, so Another comment from george and zoom in to the freedom dashboard. So it's easier to see the text in the background Uh, yeah, george. I'm actually trying to ask stuff about that. So maybe tomorrow. Um, I'll be asking How to zoom in just like in your videos and as well he said in this He said I love how you are showing the dashboard the website and the scene transitions cold effects So yeah, basically Steph is the one doing the setup here and he provided me some instructions. I'll get used to it Given some time. All right. Okay, let's see in this view with the freedom homepage I see a knot connected to in youtube live chat message in the bottom left corner If a feed is not working. I suggest hiding it Okay All right, that is very much noted And control plus on your keyboard. Oh, let's see. Let's see that.  Thank you so much for Providing me that very um, I haven't thought of that. I'm sorry Oh the live chat screen is down again. I see I'm sorry about that. Let's go ahead and check Give me a quick moment. All right, there you go. I think this would do Can you check guys? Yeah, I believe it's up again. Can you try to check? All right, so george is actually watching right now And I think he's doing his fitness regimen again I think he's just climbing the stairs or just finished climbing the stairs So maybe if you have some fitness regimen um Go ahead and have that suggested so All right, so just give me a quick second here I'll just be back for a few minutes. I'll just be fixing something here guys. Please stay tuned And I'll be right back Yes, hey guys, we are back. Sorry for that long wait and I just took a quick break here Don't worry. I'll be back. I'm already here. So we can go ahead and make sure that We can finish this by 6 p.m. So, um Yeah, basically you you just uh, just um Just uh, I just saw that george was basically in the live chat just for a little while. Thank you so much george for uh, for being here and um Yeah, so basically let's get on with the other questions that you have for freedom So from xlemc, how do I know if I send the request to join the freedom? So you just need to go to the dashboard. So your freedom dashboard. Let me just try to Let's go ahead and check here Give me a quick moment. Let me try to log into my account for you so that I can show you see you guys Give me a quick second here. It's now loading up Thank you guys for waiting So basically for you to check if you are partnered or if you have a sent in your application for freedom If you would see here You know, basically these are my two channels So this other channel that I have it's basically under review It means that you have already submitted the request from To to freedom to be partnered to be partnered with us So, um, that's what you need to look out for under review Now if you are already linked with freedom and if you're already approved of a partnership and you've and you have accepted a partnership You would see they're linked. So it's a green one then under review would be the yellow one So make sure to have your channels um Associated with your freedom dashboard so that once it's associated you can request for a review here I believe there will be an option to request for a review if basically it shows here that You have not submitted your channel for review. So just go ahead and click on it. You should be able to see if You should be able to see if if your channel is basically up for review. All right So let's go ahead and move on Okay So we also have anthony here on the live on the live stream. So just said welcome back. Hopefully to georgia's critiques and good stride, of course I I mean, it's always for improvement and I take criticism very well. So that is fine anthony. Don't worry about me. It's all good And uh, let's see here From zimran is the music provided by freedom royalty free where I don't have to say who it's by In every single video description Yes, once you are fully partnered with freedom and actually go here to music. Let me go ahead and zoom this one again for you Music, all right. If you can see that music We have several royalty free musics that are available for freedom partners. We have position music Epidemic sound and audio micro. So once you're you're fully partnered with freedom Can let's say for example, let's go to position music So let's go here. Basically their website is www.positionmusic.com Let's open up a tab here. Let's try to log in Right Okay, so basically I'm I'm automatically logged in on the account.  I'm sorry. It can't be zoom. I'm not sure why I don't know. Anyway, um, you would see there you would see in this part that you're already logged in as a freedom partner So you can search for artists and Search for albums trailer music production music licensed music since you're fully partnered with freedom You can go ahead and browse Through a wide selection of channels. So we have or a wide selection of music that you can use on your channel So Basically, that's position music So let's go ahead and check on the other one, which is Epidemic sound All right. So epidemic sound. This is their login page player dot epidemic sound comm slash login Let's click on that link for you And you would see there. This is the login page But you don't need to enter in your email address or your password What you need to do below that you would see their partner slash mcn Okay, you have a drop down there. Select freedom log in Since you have already logged into your freedom dashboard. You just need to accept that And uh, there you go Epidemic sound is here You are already logged in here And you will see there some suggested tracks From uh, from epidemic sound and you can go ahead and browse here the albums sound effects latest tracks, so You should be covered here as well and Let's go to the last one It's audio micro So for audio micro their website www.audiomicro.com slash login Basically click on that one And you should be There you go You need to sign in click on sign in And then you again you will not be using your email or username or password Because you would need to select here on the right side freedom So once you're clicking Or once you've clicked that there's going to be an authentication And uh, let's just wait for it Okay, okay, just give me a quick second my internet is quite slow I'm not sure why But it's uh, authenticating. There you go logged in see there my account you would see just type in what music you would like Maybe we can try to check chico. Maybe there's a sound effect for that or maybe a song Nah, it's not yet done So, uh, maybe uh, some of the composers out there try to make uh Any music or any sound effects with the name chico on it. Maybe I can try to use it here You may never know So basically those are our music sites for now basically for tunes. It's still on beta Um, it's a freedoms own version of music and you can also use that here So we have some uh, some tracks here as well for you and Yeah, almost the same with the three position of music audio micro and epidemic sound so You can go ahead and take advantage of this once you are fully partnered with freedom, all right Okay, so that's quite informative and as anthony said it's music discovery service and um, yeah, maybe I can do Uh, a sideline for that. But anyway, that's uh, that's gonna be for a different time so Yep, basically we are waiting for your questions guys. We have like, uh, 30 minutes left Before the stream will end again. We do want to thank you for tuning in We do want to thank you for your questions for your comments your suggestions your feedback regarding the background Regarding the stream service the stream quality What else the shirt the mug? um at your questions, of course we want to thank you for tuning in and um It's very much appreciated. Hope you hope got hope you guys can tune in tomorrow as well And uh, we'll basically be doing this again. All right so Yeah, as uh, if you can see as well on the uh chat box, uh, actually provided as well a um, a brief reminder or Yeah, a great reminder actually While you might not have to credit them. It's a good idea to list You it's a good idea to have it listed in your description in the music of your video So that viewers would like if ever viewers would like to know what is it sometimes So basically that's it. All right So zimrick, uh, we do appreciate your uh, your question. We do want to thank you for that Sweet. I'll use them right away. Thanks chico and anthony. Thank you so much as well for asking that question So that our partners would be involved as well and they would know They would know what to um They would know what what they would be getting if they would be partnered with freedom All right, so we have another question from bruno max arm roost Can I join your community team and discord if uh and discord if i'm not if i'm not yet partnered? Of course. Yes, you can always uh You can always join our community team as well as a discord server So I believe you have the links with you, but let me go ahead and provide that to you again Give me a moment Okay, here's discord And here is our community team It's always free to sign up just make sure to sign up with the community team basically our freedom Partners freedom community team will be helping you out every step of the way in regards with you developing your channel Developing your brand of promoting your brand promoting your channel improving your content growing your channel Basically, it's uh all in a positive way to help you improve overall Also the discord servers We are available there. If ever you need a quick fix if ever you are unable to let's say Watch the live stream you can do the you can do the discord We have our freedom partners and our community team logged into that they can basically help you out With your concerns, okay You're very much welcome bruno. Anyway, I'll be expecting you tomorrow as well in the live stream So keep in touch. Please, uh, you know view the live stream every now and then so, uh, you will be informed as well If ever you have questions, don't hesitate to ask. All right Okay, so Let's see I'm still waiting for other questions guys So All right, um, it's been quite a long stream today Like started 10 30 i'm gonna be ending at 6 so 11 12 1 2 3 4 5 6 like Seven and a half hours of live stream. That should be good Um There will come a time that we'll be doing this on a nine-hour shift or maybe a 24-hour shift But i'm not sure if I can do the 24 the full 24-hour shift. Maybe I would need some backup with me Maybe stuff, you know other other partners, maybe anthony, maybe george So if you would like to see that um Tell us in the comments tell us in the chat box So, um, you know, we can consider it I mean, it's gonna be a good idea if we can collaborate, right? From zen tovo. Yo, how can I become mod? So I believe you are, um, are you referring to Discord server or community team? You need to try to elaborate. Okay, so All right guys again, uh, please make sure to filter in your support questions. Uh, please no spamming as well and um Yeah, basically, let's keep this support driven so that we can answer your concerns Maybe if you have the same concern as the other one and if they basically ask that question Um, can be answered immediately So see here zimrick. I can't activate my discord on this live chat. I'm already mod on discord server Hmm, let me see that one discord server Hmm Check that out for you. I can't activate my discord on this live chat I'm already mod on discord server Okay, have you tried going to the link that I've sent? So you should be you should be able to Join in to the discord server that we have Uh, let's see Because I'm now logged in to discord Right, so we have here another question, uh, I'll go ahead and get back to use zen tovo um Oh, yeah, I just searched in zen tovo that um Actually the head chef one of the head chefs here Come on. What's up? How are you doing? Okay, from xley mc What do it means if my status in the dashboard are active and default? It means that um, it's your Active profile your active channel link that is basically linked with uh, your freedom dashboard And uh, basically active Um, that's your active channel. All right. Can I be mod in youtube live chat? Can I be mod in discord by biggie minter? All right, I think you would need to uh, you need to Ask zen tovo about the discord for the youtube live chat. Um, yeah, we'll go ahead and work things out with ashley as well So, uh, there are we're looking at it. So Let's see All right, and bruno actually provided some insights. Maybe anthony or ashley can live stream as well Or your boss forgot his name you mentioned before. Yep. My boss his name is michael pike So, yeah, maybe he can do some live streams with me here But um, I'll have to ask and I'll have to Plead for that one now. I'm just kidding. Maybe you can do that. Don't worry Okay From xlemc do it mean that I send a request I believe you would need to do so. Um, if you can go to the discord try to chat with our admins Our head chefs can actually do that. All right Okay, let's see here. Hey, I'm still waiting for your questions guys. So We are waiting for your Uh questions and score Let's see All right. So we have a message here for or from zen tobo To be head chief of the official freedom discord server You have to be active and support each other for a period amount of time Do not have any ban past reputations. So that should be good information for you Um, biggie minter. So please take note of that Okay from let's see your entertainment freedom invitation currently pause how long take it will be solved and send invitation We are having some system updates as of right now entertainment. So, uh, we are making sure that once we send out the invite It would be, um, accepted by the partner immediately so that there would be no issues and no delays Uh, we what we're looking at is basically once you accept it, um, you'll be fully fully partnered with freedom like like that, so We are working things here and if ever we are already, um, we are ready to roll out That update and once we are ready to send out the invite, um Just make sure to have your contact information updated via your freedom dashboard specifically your, um contact email address and as well as your skype just to be safe And, um, we do appreciate your patience and we do apologize for the delay But again, once we are ready to send out, uh, the invites We will certainly let you know via our newsletters and via the freedom central channel as well. Okay. Okay. Let's see here so Ah, let's see Okay, so from express crafts. I am a new youtuber. I applied but I didn't get any mail still waiting Well, I'm sorry about that express crafts. Um, have you tried making a follow-up? Uh, if you can please do so, uh with the same email that you have provided or maybe you can just create a new one Uh, please go to our support page. It's www.support.tm Um, let me just show you the website real quick There you go website basically www.support.tm You can see there open a ticket or ask the community when you open a ticket basically So make sure to include your, um, custom id your youtube channel link and as well as your, uh screenshot of your youtube feature page If ever you have to ask, uh, one of the community members for any, um, any suggestions on your channel Click on this link ask the community. You will be routed to this page It is our community team So this is our forums page. Is it quite big? No, that's that should be fine So, yep, this is our community page. You would see there the updates from our moderators and, um I just need to log in here So you should be good to go there and, um Yeah, basically you can email us directly as well at support at freedom.tm. All right Okay So let's see here and another one another question from bruno max armbus Are you in the same office with ashley? Um, unfortunately, we are not in the same office I believe she is in a different time zone and i'm in hq so Um, yeah, i'm into philippines. Ashley. I believe So it's on a it's she's on a different side of the world. So All right, but she's a good help uh in this live stream and as well and as well as in the community forum. So I do appreciate Her her efforts and as well as her um her answers in this live stream Okay, let's see here DJ harshered my channel is still under review by freedom. What I do tell me please Well, um as mentioned we are having some updates Technically or specifically uh system updates for us to be able to send in the invites properly So once we are finished with the updates We will go ahead and send you a newsletter for that or we can post a video Or maybe george can actually make a video of um Of informing you guys that the invites are up and running again So once that once that happens, uh, just look out for your email You'll be sending out an invite we're providing instructions on how to accept the invite Now we do appreciate your patience about this and we do want to thank you for staying with freedom and um Yeah, I mean we appreciate everything that you're doing with freedom And extra scraps. Thank you for your support. There's any requirements to accept my application As mentioned, there should be no, um, no copyright strikes Your channel should be in good standing no community guidelines strikes Also if um Yeah, again monetization should be enabled. We have staff demand over here And uh, what else you should have videos on your channel, of course All right, that's uh, that's good This should be done like earlier anyway And uh, yeah, I mean what else did I miss monetization should be enabled channel should be in good standing So you should be should be good to go. All right should have videos on your channel as well So that our quality control team can review your channel. Want to add something to that? Uh, no, um, just that I'm gonna steal chico now So we're gonna wrap up for today. I'm gonna give him a little bit of coaching a little bit of advice So hopefully things will be even better tomorrow. I think he's done Absolutely fantastic job today. I don't know what you guys think I hope you guys have all enjoyed like hanging out with mr. Chico And expect more things. There's lots of Lots of new graphics coming down. There's gonna be expansion to these live screens There's gonna be all sorts of really cool stuff coming down the pipeline. So, uh Yeah, I'm gonna let chico wrap up and then steal him and we're gonna have a half an hour coaching session before it's home and bed Yep thank you so much staff and um, yeah Basically, I have to wrap this up and guys again. Thank you so much for tuning in We do appreciate you being here today and uh, ashley silver does said chico did amazing today high five All right. Thank you so much, ashley. And um, again, um, I'm hoping that tomorrow We'll have another we'll have another session And um, thank you so much guys for tuning in Chico out staff out freedom out See you tomorrow guys catch you later guys


Welcome back, everyone. In this video, we're going to introduce the notion of what's called the binomial series, which is a very important Maclaurin series that represents a large family of functions. And so let's consider it here. We want to find a Taylor series centered at zero, aka a Maclaurin series, and the function and consideration is f of x equals 1 plus x to the k, where k is some, is any real number, but it's a fixed number, won't change throughout this process. Now, the reason we're going to focus on this function right here is that if we're going to have any chance of describing a Maclaurin series, the derivatives have to be somewhat predictable. And the nice thing about 1 plus x to the k is by the power rule, we can predict what those derivatives are going to be. So if you take the 0th derivative, that's just the function itself, so you get a 1 plus x to the k.  It goes down.  Then if you do the third derivative, you get a k from before, k minus 1 from before. Now you get a k plus, or k minus 2 from the previous power, and then you also times that by x, 1 plus x to the k minus 3. Like so. And if you do this over and over and over again by mathematical induction, we can see that the nth derivative of f will look like k from the first derivative, k minus 1 from the second derivative, k minus 2 from the third derivative, all the way up to k minus n plus 1 from the n minus first derivative, and then you're going to have a 1 plus x to the k minus n power. So we started off with k, and now we've subtracted n from it because we've done n derivatives. We see this pattern that follows by induction. Now for Taylor's equation, we see that the coefficient sequence inside of a Taylor series, it looks like the nth derivative evaluated at the center divided by n factorial. Great. So what we have to do is we have to evaluate these derivatives at the center, which the center is 0. Well, when you look at the at the 0th derivative, if you plug in 0, you're going to get just a 1, because 1 to any power is just k. Sorry, 1 to any power will just be 1, even if it's the kth power. With the first derivative, if you plug in 0, you're going to get 1 to the k minus 1. You'll just be left with a k. So the first derivative is k. If you plug in the second derivative, 0 takes away the x. You get 1 to any power is just 1, right? So this is the beauty here of sinuring this thing at 0. It doesn't matter, it doesn't matter what the power of 1 plus x is, is that when you plug in 0, you always get 1 to some power, which is equal to 1. And so the only thing that survived was the k and the k minus 1, which you see right here. And so for the third derivative, the coefficients will stick around. The 1 plus x will disappear.   The 1 plus x will just disappear, and you get this thing right here. And so this gives us a formula for the nth derivative of f evaluated at 0. We also needed n factorial in the bottom. So we're going to divide this by n factorial. And so what we do is we see the following formula right here. The coefficient of this, of this power series will be k, k minus 1 times k minus 2, all the way down to k and minus, or k minus n plus 1 divided by n factorial, which you see right here. And as this, this, this, this, this, this is in front of us right here, we're going to abbreviate using the following notation. You're going to put k over n and there's parentheses. The parentheses are necessary to describe this notation. It's not a fraction. There's no bar that goes between them, so no bar. So this is what's referred to as the binomial coefficient. Now, the reason it gets its name here is for the following. What if we took like 1 plus x cube, right? What if k was a positive number?  And what you can do is you can multiply this thing out. When you foil this thing, you would end up with 1 plus 3x plus 3x squared plus x cubed. And the coefficients of this sequence will look like the first number 1. This is actually 3, choose 0. The next one is 3, choose 1. The next one is 3, choose 2. And then the next last one is 3, choose 3. Where these numbers, these numbers k choose n, this actually looks like k times k minus 1. It's this formula right here. Sorry about that. Got a little messy. It's this formula right here. And because the thing is when your exponent k is a positive number, this will eventually go down to 0, right? This process eventually stops. It stops like right here. And you can actually compute the coefficients of this binomial expansion. And this is known as the binomial theorem from like an algebra class, right? So what we're doing is we're extending the binomial theorem to include powers beyond just positive integers, right? So instead of like 1 plus x cube, we're going to get a formula for like 1 plus x to the negative 3 or 1 plus x to the 1 half power. Our power of k doesn't have to be a positive integer any more. And so because of that connection to the binomial theorem from algebra, this series is commonly referred to as the binomial series. So f of x, which is equal to 1 plus x to the k, it'll be equal to its Maclaurin series, which is known as the binomial series. And you'll get the sum where n equals 0 to infinity of k over n of k choose n x to the n. This number right here is often called k choose n. k choose n. And the reason we had that before is that this is a this is a win. Again, when k is a positive integer here, you can use this to count things like, oh, I have four, you know, I have four donuts on the table and I choose to eat two of them. How many ways can I choose four donuts from two, right? So you have two donuts, you want to you have four donuts total, you're choosing four of them. How many ways can you do it? Well, you're going to get four, I guess I wrote backwards, I'm sorry, this would be, I was right the first time four choose two. So you get four choose two, and you can see there's going to be four times three over two times one, in which case you get six ways you can choose two donuts amongst the four to eat. And so that's where it gets us k choose four. This is a generalization of this binomial coefficient, this binomial theorem, and hence we call it the binomial series. This is a formula you're going to want to record later, so you can talk about these binomial series, which are pretty important. Now, with all the emphasis I put on Taylor's inequality, you might wonder, is the is the function actually equal to its binomial series? And the answer to this is that it's going to be yes. The function is equal to its binomial series. How do we see that? Well, one could do an argument, we have to determine what's the radius of convergence, first of all. One could do an argument with the ratio test a n plus one over a n, you can see that right here. If you take a n plus one, you get this thing right here. If you take one over a n, you get this thing right here. Putting the factorials together, you get n factorial over n plus one factorial, that'll simplify just to be one over n plus one. If you take this k, k minus one, k minus two, all the way to k minus n, and you divide that by k, k minus one, k minus two, all the way to k minus n plus one, most of those things will cancel out, right? You get k cancel, k minus one cancels, most of these things are going to cancel out with exception of, whoops, I canceled the wrong one, everything except for the k minus n should cancel out there. As soon as I did all those things correctly, no, I think I, I think I, I think I botched that. The one on, let's see, the one on, which is the bigger one, the one on top is the biggest one, right? Because k minus n plus one, that's the biggest number, so it didn't have anything to cancel out there, so there should be like a plus one in there. It looks like it's a typo. And so then the x's will also cancel out, leaving you just an x.  You get one over n plus one times k minus n plus one times x, and so you get a plus one right here again. Now taking the limit, this typo seems to exist forever for the rest of this thing. So as you take the limit as n goes to infinity, you're going to see that this thing is just equal to the absolute value of x, things will cancel out. And I can show you some more, again, there's some typos here, so don't worry about that too much, I'll fix these in the lecture notes that you can see linked to this video. But this thing will go off towards x, and this is with the ratio test, so we need x to be less than one. This tells us that the radius of convergence is one, so the function only is, well the radius of convergence for the series here is going to equal one. There are some exceptions to that, of course. What happens when x equals one? What happens when x equals negative one? It kind of depends on the k value. It depends on k. Of course, like if k is a positive integer, actually the radius of convergence is infinity because it's just a polynomial in that case, but for other values, it'll be one. And whether it converges at one or negative one depends on k. And we'll see an example of this just a moment. And you can use Taylor's inequality to show you that the function is equal to the binomial series. What I want to do here is do an example of actually computing the binomial series for a specific function. Let's take the function f of x equals one over the square root of four minus x. And I do want to convince ourselves that this is a binomial series here. So f of x equals one over the square root of four minus x. Notice that you can first of all factor out of four, right? Because with the binomial series you want a one plus x. We have a four minus x. How do you deal with that? So we're going to factor out of four that leaves behind one minus. We want a plus there. So we're going to get one plus a negative x over four. This all sits below one. The square root of four is two. So we get a one half that sits out in front. And then the square root is the one half power. So we're going to get one plus a negative x over four. And then the square root is the one half power. And since it's a denominator, we get a negative sign. So we're going to get a negative one half right here. And so this tells us we have a binomial series with a k value of negative one half. And we're going to substitute u with a negative x over four into our series. So our function f of x is going to equal one half times the sum where n ranges from zero to infinity. We're going to get the binomial coefficient negative one half choose n. And then we're going to get negative x over four raised to the nth power. If we plug that into the formula right there. And this right here gives us the series we could stop here if we really wanted to. But if you unravel the binomial coefficient a little bit, what you're going to see is the following. You're going to get one half. Then you're going to times that by, again if you write this, write this thing in expanded form, you're going to get one, right? One thing you should know about binomial coefficients is that if you take k choose zero, k choose zero, this will look like, well you, what was the original formula again, right? You're supposed to take no terms, you have no terms, you get a one over zero factorial, which is going to just equal one. k choose zero is always a one. k choose one, that's going to be k over one factorial, that's always just equal to k. Other ones are a little bit more difficult to do, but like if you do k choose two, you end up with k times k minus one over two factorial. I just kind of continue with that pattern there. So you're going to end up with one plus negative one half you get from the binomial coefficient. Then you're going to get a negative x over four. We'll come back to that one just a moment. Then the next term you're going to get k choose two, which that thing is going to look like negative one half on top. You're then going to get negative three halves for k minus one. This sits above two factorial, which is just two, times that by negative x over four squared. The next term we would get negative one half times negative three halves times negative five halves. This last term is k minus two. This sits above six, which is three factorial. And then we're going to get negative x over four cubed. And this pattern will continue on and on and on. I think we have enough to figure out what's going on here. So notice some things that are going to happen. Again, the one half sits out in front. We get this one. We get minus. We'll actually get plus negative negative, right? We get plus. We're going to get x on top and eight on bottom. The next one we're going to get minus, minus, and then and then so the negatives here cancel out. And then you're squaring a negative. So it's also a plus. So you're going to get a plus. You're going to get one times three, which is three. You're going to get an x squared. And on the bottom, you end up with a two. You get a two. You get a two. So that's eight. And then you get four squared, which is 16, right? So in that situation, what do we have? We get four times eight times 16. That looks like a big one. We'll come back to that one later. For the next term, what's going to happen here? You're going to get negative, negative, negative times negative, negative, negative, right? That's going to be a positive as well.  So that's a 15 on top. You're going to get x cubed. And then you're going to get a two, a two, a two. So that's, there's eight there. You're going to get four cubed. That's a big number times six. So you get like eight times six times four cubed. And this kind of continues on and on and on. And so again, trying to describe the general solution, because you can also distribute this one half through if you want to, but I'm going to leave it out factored. So in general, if you want to describe this without the binomial coefficient, this would look something like n equals zero to infinity. What you're going to see at the top is you see this factorial like object, one times two times five times, keep on going. But what you do is you don't get every number like a factorial does. You actually end up with only odd numbers. So you get like this odd factorial, one times three times five times seven times nine times 11 up to wherever you terminate at, which will be two n minus 11. In the denominator, you're going to end up with an n factorial. That came from like the two factorial, the three factorial we see right there. But what else are we getting here? We're getting a bunch of twos that are popping up everywhere, because every time we do another k minus whatever, we're going to get a multiple of one half, which those gather together to make some eights. But we also can combine it together. We can also combine it together with the powers of four we have. And so in the end, it turns out that you're ending up with eight to the n in your denominator x to the n. So if you keep track of all the twos there, we should have eights or like what we had here is you had an eight, right? And keep on going from that. And so then our formula in the end should look something like this. Again, I went through that kind of a little bit quickly, because honestly, when it comes to these binomial coefficients, really, really, what we like to do is we just like to use the binomial coefficient formula, right? I mean, that's what we have. That's what we have this abbreviation to keep track of all these things. This is a pretty, this is a perfectly good way of expressing it. If you want to do it in expanded form, you can do something like this. I went through it kind of quickly. So I apologize if someone got a little bit confused. The intention isn't necessarily to get to this formula. And I'm actually quite good, quite, quite happy with everyone using this formula right here. This is perfectly fine. What we need to finish off, though, is we actually have to deal with, I mean, it's kind of interesting to see that this thing's actually not an alternating series, because you have this negative one to the n right here, you think that's alternating, but this negative k here also is alternating, so they actually balance each other out. What we want to finish off with is with the radius of convergence, because what we saw before is that negative x over four, much like a geometric series, it needs to be less than one. And so this would imply that the absolute value of x over four is less than one. So this tells us that the absolute value of x should be less than four, which this is our radius of convergence. So this binomial series will converge with the radius of convergence of four. And so that shows us how one can deal with a binomial series.


What's going on guys welcome back to another video if you guys are new to the channel make sure you guys hit that subscribe button Today's video is going to be absolutely crazy before we get into it guys Janice and I have been dropping a ton of vlog content on our vlog channel We've recently made a vlog channel and we've been going crazy on it So if you guys haven't already checked it out Make sure you guys go subscribe to that channel if all you want to see is just lit vlogs and see like the real real Us it's a very transparent channel. We're showing you guys are like day-to-day life It's honestly super crazy, and it's been lit so far So make sure you guys head over to Janice and Isaiah vlogs and go subscribe But as you guys can tell by title and thumbnail the video today, you boy We've been going so hard on the vlog channel that I feel like I haven't had enough time to really get her mad and really You know do what I do best so today this morning I woke up and I'm like, you know what before going to our workout, you know before we hit the gym or whatever I was like, you know what? Let me get this banger out as guys can tell by title and thumbnail the video Your boy is gonna be hiring because I'm not gonna really do it I'm gonna be hiring a hot cleaning lady to come and clean the house because truth be told guys We've been really really busy lately like we have a lot of like personal life stuff going on Then on top of that we're trying to run this channel trying to run our vlog channel and then stay on top of tiktok It's just a lot that we don't really have that much time to clean like we do our best But the house could be cleaner truth be told so I don't know if you guys can see but we have a huge like It's not it's not huge, but we have like a lot going on over there at the counters It's really not as clean as it's supposed to be and the living room right now is actually clean But your boy is gonna tear it up. I'm throwing bloopers toys all over the place. I'm gonna have some pillows on the floor I'm gonna throw the blankets on floor I'm just gonna make this look like a complete mess to justify me telling my fiance We need to hire a hot cleaning lady like this Now when I showed Janice this picture she is going to flip out I already know her you guys already know her so if you guys are ready for today's video Make sure you guys smash that thumbs up button comment down below team Isaiah all day every day and let's get into it It's been too long. It's been way too long All right, so like I said guys I made a huge huge mess There's just stuff all over the place bloopers probably love and he's playing with all his toys right now But I'm also gonna show you guys everything we have going on here Like all this stuff is supposed to be like in the pantry in the fridge and like why do we have mouthwash down here? Like you know what I mean like I don't know This is all just gonna justify why I need to hire this hot cleaning lady, but let's get into it Hey, hey What all right, so before we go to work out I want to bring this up to you Bring what up cuz I feel like we've been slacking Slacking. Yeah. Oh I'll explain this in a second made to order She's a major order. I'll explain this in a second Hold on First of all, what is that?  I don't know. That's not what I found her for That's what you found her for. No, I found her. First of all, why are you looking for maids? Okay, first of all, can I like get a word out before you started going crazy on me? Like look around the house. Look at the counter. Why is all this stuff here? Why is because I had to make something giving what with mouthwash, but I just thank you Okay, but why is it also here like this stuff has been here for two days already. I know it has I said I just ordered this this morning, so you're all this this morning. Yes. Oh, this is say is this that's for my aunt the game That's for the kids when they come The low-drive. Yeah, I'm straining my hair bow later doing too much. I'm doing too much. This this isn't clean I'm not blaming it on you. I'm just saying that we have to start putting stuff away We gotta start cleaning more like look at this stuff over here. We have random curtains Slippers and just bags sitting there and then look at the living room. He took all his toys this morning But I know when he gets to zoomies.  I could clean all this by myself We have dishes like three doesn't matter. We don't need a man Babe, we need a cleaning lady. It's the last time we swept and mop you sweet mom Like when I can yes, but it's been a while I haven't even vacuumed in a while to like I feel like it's mad dusty in here, too Like I feel like we were not on top of everything we need to be on top of well cuz we be busy like I mean But when we need to clean we clean I get it like I said, I'm not but we don't need this like I said What are you talking about? Yes, we do look She said made to work right and she's available. She's been qualified. She's been doing maid services for six years already She has number good. She has about four. I think it was like 4.8 stars on Google Babe, why are you worrying about how she looks? I don't Babe, that is they made she's a maid What does it matter if she has it out or not? I don't care for that. What do you mean? You don't care for that. He had good reviews. So I picked her it's not my fault that you think she looks some type of way Why are you worried about how she looks anyway? Stop worrying. Well, it's not that look at how she's dressed Why does it work? She's gonna do I can simply go upstairs if that makes you uncomfortable where her reviews are like on point and No one else had good reviews like her She's the best maid around the area in the Tampa area. She is the best me bro.  All right, uh-huh You see not only spots anywhere on your body or anybody else.  What do you mean? I'm not saying she's gonna come over here and try to like hit on me or I'm gonna try to hit on her Like I don't I just want the house clean. It's all I can't I'm telling you that that's not what she does Are you know because because she's dressed like that. That's why that's why you know, how do you not seem like role? Wouldn't she be advertising herself as that person that she's advertising herself as a real maid She's not a real maid, babe. She has a whole costume on it like she dressed up for Halloween How do you know that's just not her uniform?  Are you gonna be that person?  Sexy maid for her before Obviously not So how do you know she works like that? How do you know she's not a roommate? She just like I already booked her She comes next Saturday Saturday morning 10 a.m. She will be here How are you gonna book her without telling me something about her because if we if I haven't talked to you body It's gonna drag it even longer, but I just want the house clean bro. Like that's all I care I just wanted to be clean. I'm tired of seeing First of all long goes that that was I did that I did hit up the first person We actually had a clean lady for when we moved in no, she's living now Honduras. You're lying.  What what you want to hit her up yourself.  I'm willing to like help you clean away And I'm not pinning it on you, but if you I'm trying to fix the problem, and you don't want to You're not trying to fix the problem You trying to hide a hooker to come sit at house and give you something like oh my god Like I said, I will go upstairs and be away from her if that's what you want. I don't care I just want the house clean I just don't like how you went behind your back and booked her without talking to her I went behind my own back. I went behind your back first of all You were to that wrong.  You're not even making sense anymore.   Look another thing. We got clothes.  Yes We have a lot of we have a lot of things planned messing. I have a confession what I made that mess. I know you did I blame it on our son No way he would do all of that Are you always under the bed come here? Baby So yeah guys that is it for today's video I hope you guys enjoyed it her reaction team Isaiah further when you got anything you want to say Maybe call yourself a loser What I mean say guys hope you guys enjoyed it comment down below team Isaiah all day every day with that being said We'll see you guys in the next video


Welcome to Unit 2 of Professional Writing. Now that you've determined your audience crafted your main point and created an outline, it's time to draft your message. In this unit you'll learn how to reinforce your main point and persuade your audience while avoiding the common errors that can distract your readers. A first step is to connect with readers through a personalized salutation, like Dear Mr. Smith or Dear Sales Team. Calling your audience by name lets them know the message is for them and it goes a long way toward making your writing work. Next, you'll work on drafting a message that consistently supports your main point, in the subject line, the title, section headers, and in-topic sentences. More than this though, you'll learn how to create a clear, compelling story in your writing, conveying complex ideas in a way your readers can easily comprehend. And you should be compelling, but also fair, with your audience and with your sources. So in the last part of this unit, we'll look at some of the ethics of writing, using appropriate sources and giving credit for words and ideas that are not your own. When you're done with this unit, you'll have a complete draft ready. The learning and the writing should take about an hour and 20 minutes to complete. Good luck.


iedy  Janet Nuslam� vela village Cloud continues trials 1.1.2, Due to physical strain 1.2.6 will start increasing 2.8 2.8 3.0 2.8 4 watch 4 watch


I just put up two Harbors City skate parks, probably one of my favorite Los Angeles County skate parks meeting up with Matt Digi. I've been in contact with Matt for like, like since like the mid DIY diaries stuff. Spring break guys. He's on spring break out here. So yeah, whatever spring break is. I'm not sure what spring break is. Straight off the plane to board sliding up a key crow. Oh, there it is. That's like third try dude. So sick man. Dude, it's waxed enough. You got that Cali wax. Yep, always. Which one the East Coast, so things aren't there out and waxed apparently. So if you're not subscribed to Matt's channel, head on over, give him a sub. Some cool East Coast. He did add some snowboarding content. Skateboarding, snowboarding. What do you mean it did bad? That video did bad. Really? I thought it was cooler because it was like, it was in rail gardens. That's like a different spot. What that spot was you guys were riding. Oh, it's like, bro, it's like the same thing. Railgarns in Utah.  Oh, okay. It's on campus. I call it the railgarns because it looks like it. But it was sick to watch you guys like groom the spot and then ride it. Yeah. It's cool to see. It was a lot of work. Yeah. But yeah, head on over, subscribe to his channel. And yeah, you'll probably see him back on the West Coast. Yes. In the summer or something. Every three months or so. Yeah. Oh, yeah. All right. So you guys have been probably wondering and asking and commenting and messaging me about this for the longest time. You guys want to know what happened to my eye. And before we get into this, I didn't do this myself. I didn't purposely like people think I tattooed my eye. I didn't tattoo my eye. People think that I've done this to myself. I didn't do this to myself. I can still see perfectly fine. And yes, I have been offered the opportunity to get them lasered, surgery out, lasered, surgery out. I've had the opportunity to get them lasered out when I was a small child. I just never did it because I didn't feel like it was a big deal to me. The truth is one of them is a birthmark. I can't remember which side it is. I think it's the inside is a birthmark, maybe. I don't know. One of them is a birthmark. I share the same birthmark with my grandpa, so my dad's dad. He has the same birthmark in his eye. But I'm pretty sure it's the outer one. I did have an injury and cop this kind of brutal, nasty blood clot. It's not really a blood clot, but it's like a scar in my eye. I think I was about four at the time, four years old. This is when we were staying with my aunt in Ontario. Is that how you pronounce it? Ontario, the one in California, not the one in Canada. And I can't remember who it was with. I'm pretty sure at the time my aunt was kind of like a foster parent. So she had some foster kids that she was looking after at the house. And I was like four years old. So we were outside playing hide-and-go-seek or something. I remember we were playing some type of hide-and-go-seek game or hide-and-go-seek tip. I don't know. And there was this bush that I was hiding behind. And I was squatting down, hiding behind this bush. And for some reason, I have no idea why I was doing this. But I was kind of crouched down. And I was rocking back and forth, back and forth. And each time I rocked back and forth, my face and eye came closer and closer to this branch. Don't ask me why I was doing this. I don't know why I was doing this. Anyway, I rocked a bit too far forward. I lost my balance. And I literally seen this branch, this twig, like come right at my eye and like stab me in the eye. And I screamed and I was crying and whatever else. Ran back to the house and they're running water and stuff over my eye to make sure it's like, you know, I didn't stab myself in the pupil or whatever. But yeah, that happened. This came about, I think they wanted, I think they did take me to the urgent care. I can't remember, I was four years old. They might've taken me to the urgent care or they rang someone or they were trying to get medical advice. They kept running water underneath it. But it ended up healing like this. And I have been offered the opportunity to get it removed. As I said, back in Australia, I've been given the opportunity to get it removed. But I'd need to take laser eye surgery. And I didn't want to do something like that. I would've been like four or five years old. I didn't want to get laser eye surgery because I'm still a kid and I'll have to rock an eye patch for God knows how long. So I didn't really want to do that. So we kind of left it, but they recommended that we get it checked out every so often, especially because I was a growing, young, growing boy that were like, we need to make sure that it doesn't slide over your pupil, which it won't, because it's like a scar in a layer of my eye that's like underneath and away from the people. But as I've aged, they've both come closer towards the center. I don't know if that's because of my eye, how my eye's grown, or they've shifted or whatever, but they've both become like closer to the center of my eye, let's say my pupil. I can't remember what percentage of the world has birthmarks in their eyes. Some people get birthmarks where it's like half their pupil is a different color to the other half, kind of like those huskies, husky dogs, you see they have like a double colored pupil, if you will. I do know people go and get their eyeballs tattooed. Believe it or not, that's actually done with a syringe. So they get the syringe, they fill it up with ink. For God knows why they want to do this to themselves. And the syringe penetrates a layer of the eyeball where you can inject the ink and it'll kind of spread like a jelly pen, like the ink will just kind of spread. So they end up doing it like a few times. I'll do it like one, two, three to make sure your whole white of your eyes turns it into blue or green or God forbid black, which some people do. I haven't done that and I'm not high. That's another question I get all the time is, are you high because I have these things in my eye? People think I have red eyes from smoking, but I don't really get offended. People ask me, oh, like I don't mean to ask this question, but what happened to your eyeball or like what happened for that to become like that? Like people get super, super cautious about asking me and like I didn't care. I forget it's there to be honest. I only realized it's there when you guys comment, hey, I don't mean to be rude, but what happened to your eye or if you guys are OG viewers of the channel, you guys would have seen, I made a video on this like ages ago, back in Australia. So if you guys know, if you guys are OG viewers of the channel, you know what happened to my eye, but if yous aren't then this is what happened to my eye. One side is a birthmark, one side is a scar, and they don't affect my vision and they don't hurt. I know it looks like they hurt because they're just so big and brown and red, but it actually doesn't hurt. I can't, I can't feel it. I could feel it obviously at the time when I got stabbed in the eye with a stick, but I can't feel it, it doesn't affect my vision. So far it's been all right. The optometrists or the doctor or whatever did tell me try to avoid a lot of light coming into your eyes. So I think this is more when I was a teenager there, I would wear sunglasses a lot purely because I thought that the sun would get into my eye and then make them bigger. I don't know if that's a real thing, that's what they told me, but I don't really sweat on it anymore. Like I don't, it doesn't affect me in any other way as any other part of my body having a birthmark on it, if that makes sense. And I'm sure everybody gets those eye floaters. You know, you'll be like looking into the sky and you'll see those little clear eye floaters come across your vision like this and every time you try to look at them, they move, they're like little worms almost. I have those, but a lot of people have those. I'm not sure if it's to do with my vision because believe it or not, I wear reading glasses and it's this eye that has the stigmatism. So if you guys don't know what a stigmatism is, it's basically the shape of your eyeball. It's not a perfect like circle or sphere. It's more of an oval shape like a football. So this is my bad eye, believe it or not. So I wear glasses for this eye, but I think having the floaters has something to do with my eye shape being a weird shape. I don't know. I've only been to the optometrist like two or three times in my life. That's what happened to my eye. Hopefully you guys will watch this video and listen to what I'm saying about what happened to my eye. If not, it's fine. Just when you comment, what happened to your eye? It's just like, I don't know. I've written out comments a hundred different times now explaining. So I thought I'd make a video just to update you guys on what happened to my eye. But yeah, that's pretty much it. If you guys are new to my channel, make sure you subscribe, check out eveningmob.com. We just got a bunch of the throwy hoodies reprinted. We got tote bags as well. They're pretty sick. We have, what else do we have?  It's coming into summer. You need a nice pair of sunnies to protect your eyes from the harmful UV rays because there's holes in the ozone. I don't know if holes in the ozone affect the amount of UV rays. I'd imagine they would. But yeah, I'm gonna stop babbling on. Hopefully you guys enjoyed this video. I'll catch you guys in the next one. On your way back, bring me his son. On, on, on, on your way back.


running of this very event and I would like to say this day possible. Dinkston Distillery, who donate bottles of whiskey, one of which I think is going to be poured into the river. Not the whole bottle, it's not the whole bottle. Thank you for that. Monaco More Hotel and the Lewis family who helped with our catering as do Campbell's. Dingling Active, who kindly donate our media and marketing and the Dunandinstone Pipe Band, I think they deserve a round of applause. Sterling Council. Well this morning was a real privilege for me to be able to open this salmon season on the teeth. As everybody knows the teeth is a migratory fishery of excellence. It has international status, SAC and of course the government has classed it as a class one fishery. Particularly pleased to open it because I'm a great supporter of Sterling Council's fishery team. They've done so much over the years to promote conservation and best practice. And one of the projects this year is to make it the year of the youth. And that's really important to me because the youth are the caretakers of the river in the future and our future anglers. So I very much support that. I'm very pleased that my family is associated with the river because the river, especially the river teeth, has been a big part of my life through fishing. I'm particularly keen on fishing for sea trout at night. I'm very pleased to see my granddaughter who's only, she's just coming up for seven. She's interested, she's got her own wee rod and all the rest of it. And her dad, my son-in-law, I consider to be one of the, a really, really excellent flyfisher and I believe that he's going to pick up a prize tonight at the dinner. And while the teeth itself is well known for its fishing and all the rest of it, there are one or two problems that we really need to talk about. And for me who stays, my front door is 60 yards from the river and I'm down at the river on a day-to-day basis seeing what's going on. And one of my concerns over the last two or three years is the increase in population on sawbills, mergansers, cormorants and things like that. And the reason I want to talk about this, it's a controversial subject. Species conflict is always, you know, it's difficult. But the fact of the matter is that there's far too many of our smokes are getting eaten before they get anywhere near the sea. And that to me is a big concern. Now surely 2018, surely we can all get together, both sides can get together and with a wee bit of compromise and a wee bit of collaboration we can find a way forward. I'm certainly not advocating that we should go out and shoot them or anything like that. That's against the law and that's not what I'm saying. But what we need to do is to talk about it. There should be no winners, there should be no losers in this, but now is the time that we need to talk about it.