Answer
$\dfrac{1}{1+x}$
Work Step by Step
The sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}$
The given series $\sum_{n=0}^\infty (-1)^n x^n=\sum_{n=0}^\infty (-x)^n$ shows a convergent geometric series with first term, $a=1$ and common ratio $r =-x$
$S=\dfrac{1}{1-(-x)}=\dfrac{1}{1+x}$
Hence, the given series converges to $\dfrac{1}{1+x}$ for $|x| \lt 1$
