Answer
converges to $\dfrac{1}{2+x}$ for all $|x+1| \lt 1$ or, $-2 \lt x \lt 0$
Work Step by Step
Formula to calculate the sum of a geometric series is:
$S=\dfrac{a}{1-r}$;
Here, $a=1$ and common ratio $r =-(x+1)^n$
$S=\dfrac{1}{1-(-(x+1)^n)}$
or, $S=\dfrac{1}{2+x}$
Hence, the series converges to $\dfrac{1}{2+x}$ for all $|x+1| \lt 1$ or, $-2 \lt x \lt 0$
