Answer
converges to $\dfrac{2}{x-1}$ for all $|\dfrac{3-x}{2}| \lt 1$ or, $1 \lt x \lt 5$
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 $r =\dfrac{3-x}{2}$
$S=\dfrac{1}{1-(\dfrac{3-x}{2})}$
or, $S=\dfrac{2}{x-1}$
Hence, the series converges to $\dfrac{2}{x-1}$ for all $|\dfrac{3-x}{2}| \lt 1$ or, $1 \lt x \lt 5$
