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
The sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}$
We have a convergent geometric series with first term, $a=1$ and common ratio $r =\dfrac{3-x}{2}$
$S=\dfrac{1}{1-(\dfrac{3-x}{2})}=\dfrac{2}{x-1}$
Hence, the given series converges to $\dfrac{2}{x-1}$ for all $|\dfrac{3-x}{2}| \lt 1$ or, $1 \lt x \lt 5$
