Answer
$\dfrac{e^2}{e^2-1}$
Work Step by Step
Here, $a=1$ and common ratio $r =\dfrac{1}{e^2}$
Formula to calculate the sum of a geometric series is:
$S=\dfrac{a}{1-r}$
Thus, $S=\dfrac{1}{1-(\dfrac{1}{e^2})}$
or, $S=\dfrac{e^2}{e^2-1}$