What is the value of \[1+2+3-4+5+6+7-8+\cdots+197+198+199-200?\]
Looking at the numbers, you see that every set of $4$ has $3$ positive numbers and 1 negative number. Calculating the sum of the first couple sets gives us $2+10+18...+394$. Clearly, this pattern is an arithmetic sequence. By using the formula we get $\frac{2+394}{2}\cdot 50=\fbox{9,900}$.