#### Answer

The series converges and its sum is $\frac{5}{\pi-1}$.
Now To reach that we observe that the intial term is $\frac{5}{\pi}$ and the common ration |$r$| = $\frac{1}{\pi} \lt 1 $ .
And Such case according to definition 4 in page 750:
$S= \frac{a}{1-r}$ = $\frac{\frac{5}{\pi}}{1-\frac{1}{\pi}} = \frac{5}{\pi-1} $

#### Work Step by Step

The steps of the answer are written in detail in the following image.