Answer
Converges and sum is $S= \frac{5}{\pi-1} $
Work Step by Step
The series converges and its sum is $\frac{5}{\pi-1}$.
We observe that the intial term is $\frac{5}{\pi}$ and the common ration |$r$| = $\frac{1}{\pi} \lt 1 $. $$S= \frac{a}{1-r} = \frac{\frac{5}{\pi}}{1-\frac{1}{\pi}} = \frac{5}{\pi-1} $$
