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Problem: |
Compute the following expression: $\sum_{k=0}^7 -\frac{100}{33}10^k$ |
Answer: |
$-\frac{101010100}{3}$ |
Problem: |
Compute the following expression: $\sum_{k=0}^7 -\frac{62}{3}\frac{1}{8}^k$ |
Answer: |
$-\frac{24766365}{1048576}$ |
Problem: |
Compute the following expression: $\sum_{k=0}^5 -\frac{73}{42}\frac{1}{5}^k$ |
Answer: |
$-\frac{6789}{3125}$ |
Problem: |
Compute the following expression, or identify that it diverges: $\sum_{k=0}^\infty \frac{2}{55}\sqrt{5}^t$ |
Answer: |
$\text{Diverges}$ |
Problem: |
Compute the following expression: $\sum_{k=0}^10 -\frac{7}{34}\frac{1}{32}^k$ |
Answer: |
$-\frac{8135534810733799}{38280596832649216}$ |
Problem: |
Compute the following expression: $\sum_{k=0}^4 \frac{41}{83}\frac{1}{32}^k$ |
Answer: |
$\frac{44378441}{87031808}$ |
Problem: |
Compute the following expression: $\sum_{k=0}^6 \frac{71}{96}\frac{1}{\sqrt{3}}^k$ |
Answer: |
$\frac{355}{324}+\frac{923}{864 \sqrt{3}}$ |
Problem: |
Compute the following expression: $\sum_{k=0}^9 -\frac{44}{43}\sqrt{5}^k$ |
Answer: |
$-\frac{34364}{43}-\frac{34364 \sqrt{5}}{43}$ |
Problem: |
Compute the following expression: $\sum_{k=0}^5 -\frac{25}{18}7^k$ |
Answer: |
$-\frac{81700}{3}$ |
Problem: |
Compute the following expression: $\sum_{k=0}^13 -\frac{11}{27}\frac{1}{32}^k$ |
Answer: |
$-\frac{139639869117113164921}{332041393326771929088}$ |
Problem: |
Compute the following expression: $\sum_{k=0}^\infty \frac{42}{47}\frac{1}{32}^k$ |
Answer: |
$\frac{1344}{1457}$ |
Problem: |
Compute the following expression: $\sum_{k=0}^\infty \frac{76}{89}\frac{1}{6}^k$ |
Answer: |
$\frac{456}{445}$ |
Problem: |
Compute the following expression: $\sum_{k=0}^6 \frac{4}{7}\sqrt{5}^k$ |
Answer: |
$\frac{624}{7}+\frac{124 \sqrt{5}}{7}$ |
Problem: |
Compute the following expression: $\sum_{k=0}^10 -\frac{25}{18}\frac{1}{7}^k$ |
Answer: |
$-\frac{8238861425}{5084554482}$ |
Problem: |
Compute the following expression: $\sum_{k=0}^\infty -\frac{7}{45}\frac{1}{\sqrt{7}}^k$ |
Answer: |
$\frac{49}{45 \left(\sqrt{7}-7\right)}$ |
Problem: |
Find the inverse of the following function: $\log (8-4 x)$ |
Answer: |
$\left\{\left\{x\to \frac{1}{4} \left(8-e^y\right)\right\}\right\}$ |
Problem: |
Find the inverse of the following function: $\sqrt[3]{-8 x-\frac{13}{3}}$ |
Answer: |
$\left\{\left\{x\to \frac{1}{24} \left(-3 y^3-13\right)\right\}\right\}$ |
Problem: |
Find the inverse of the following function: $\sqrt[3]{\frac{5 x}{2}-\frac{17}{2}}$ |
Answer: |
$\left\{\left\{x\to \frac{1}{5} \left(2 y^3+17\right)\right\}\right\}$ |
Problem: |
Find the inverse of the following function: $e^{\frac{23}{5}-\frac{39 x}{5}}$ |
Answer: |
$\left\{\left\{x\to \fbox{$\frac{5}{39} \log \left(\frac{e^{23/5}}{y}\right)\text{ if }y>0$}\right\}\right\}$ |
Problem: |
Find the inverse of the following function: $\cos ^{-1}\left(\sqrt{x-7}\right)$ |
Answer: |
$\left\{\left\{x\to \fbox{$\cos ^2(y)+7\text{ if }0<y<\frac{\pi }{2}$}\right\}\right\}$ |
Problem: |
Find the inverse of the following function: $\sinh \left(\frac{11 x}{2}+1\right)-\cosh \left(\frac{13}{2}\right)$ |
Answer: |
$\left\{\left\{x\to \frac{2}{11} \sinh ^{-1}\left(y+\cosh \left(\frac{13}{2}\right)\right)-\frac{2}{11}\right\}\right\}$ |
Problem: |
Find the inverse of the following function: $\sin ^{-1}\left(\frac{9}{2}-\frac{9 x}{2}\right)$ |
Answer: |
$\left\{\left\{x\to \fbox{$\frac{1}{9} (9-2 \sin (y))\text{ if }-\frac{\pi }{2}\leq y\leq \frac{\pi }{2}$}\right\}\right\}$ |
Problem: |
Find the inverse of the following function: $-\tan ^{-1}(8 x+3)$ |
Answer: |
$\left\{\left\{x\to \fbox{$-\frac{\tan (y)}{8}-\frac{3}{8}\text{ if }-\frac{\pi }{2}<y<\frac{\pi }{2}$}\right\}\right\}$ |
Problem: |
Find the inverse of the following function: $\cosh \left(\sqrt{6 x+9}\right)+1$ |
Answer: |
$\left\{\left\{x\to \fbox{$\frac{1}{6} \left(\cosh ^{-1}(y-1)^2-9\right)\text{ if }y>2$}\right\}\right\}$ |
Problem: |
Find the inverse of the following function: $\tanh \left(\tan ^{-1}(7 x+3)\right)$ |
Answer: |
$\left\{\left\{x\to \fbox{$\frac{1}{7} \tan \left(\tanh ^{-1}(y)\right)-\frac{3}{7}\text{ if }-\tanh \left(\frac{\pi }{2}\right)<y<\tanh \left(\frac{\pi }{2}\right)$}\right\}\right\}$ |
End of preview.
To cite the dataset please reference it as
@article{hendrycksmath2021,
title={Measuring Mathematical Problem Solving With the MATH Dataset},
author={Dan Hendrycks and Collin Burns and Saurav Kadavath and Akul Arora and Steven Basart and Eric Tang and Dawn Song and Jacob Steinhardt},
journal={NeurIPS},
year={2021}
}
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