part $1$ of $2$

$($i$)$ Find all values of $x$ for which the series

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(x-3{)}^n}{5^n}$

onverges.

part $2$ of $2$

$($ii$)$ Find the sum of the series for those values of $x$ for which it converges.

converges only on $(-2,8)$

converges only on $(-8,8)$

converges only on $(-5,5)$

converges only on $(-2,2)$

converges only on $(-8,2)$

${\displaystyle \underset{?}{\overset{?}{}}}=\frac{x+3}{2-x}$

${\displaystyle \underset{?}{\overset{?}{}}}=\frac{x}{5-x}$

${\displaystyle \underset{?}{\overset{?}{}}}=\frac{2-x}{x+3}$

${\displaystyle \underset{?}{\overset{?}{}}}=\frac{8-x}{x-3}$