## Calculus 8th Edition

$\sum_{i=0}^{n}(-1)^{i}x^{i}$
We contract the sum into sigma notation by noting that it follows the pattern of a sum of powers of $x$ (e.g. $x^i$), starting with $1=x^0$ (e.g. $i=0$) and ending with $x^n$ (e.g. $i=n$). In addition, the sign of the terms alternates, so we include $(-1)^n$: $1-x+x^{2}-x^{3}+\displaystyle \cdots+(-1)^{n}x^{n}=\sum_{i=0}^{n}(-1)^{i}x^{i}$