Answer
$\dfrac{\pi}{\pi - e}$
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 $r =\dfrac{e}{\pi}$
$S=\dfrac{1}{1-\dfrac{e}{\pi}}=\dfrac{\pi}{\pi - e}$
Hence, the given series converges to $\dfrac{\pi}{\pi - e}$.
