# Thread: Power series

1. ## Power series

I need to prove this(not sure how to):

$\sum_{n=0}^{\infty}{{(-1)^n}{x^n}}$ = $\frac{1}{1+x}$

2. Hello,

Originally Posted by kezman
I need to prove this(not sure how to):

$\sum_{n=0}^{\infty}{{(-1)^n}{x^n}}$ = $\frac{1}{1+x}$
$\sum_{n=0}^\infty (-1)^nx^n=\sum_{n=0}^\infty (-x)^n$

Assuming that $|x|<1$ and noting that this is a geometric series, what can you conclude ?