Answer
converges to $\dfrac{1}{1-2x}$
Work Step by Step
The sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}$
The given series shows a convergent geometric series with first term, $a=1$ and common ratio $r =2x$
$S=\dfrac{1}{1-2x}$
Hence, the given series converges to $\dfrac{1}{1-2x}$ for all $|2x| \lt 1$ or, $|x| \lt \dfrac{1}{2}$
