## Calculus 8th Edition

$0$
We expand and simplify the sum. We note that the terms alternate from -1 to 1. Since there are an even number of terms, the sum is 0. $\displaystyle \sum_{n=1}^{20}(-1)^{n}$ $=-1+1-1+1-1+1-1+1-1+1-1+1-1+1-1+1-1+1-1+1$ $=0$