Answer
Divergent
Work Step by Step
The sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}$
The given series has first term, $a=1$ and common ratio $r =|\dfrac{e^\pi}{\pi^e}|=\dfrac{23.141}{22.459}$
Hence, the given series diverges because $|r|=|\dfrac{23.141}{22.459}| \gt 1$
