## University Calculus: Early Transcendentals (3rd Edition)

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 $|r|=|\dfrac{23.141}{22.459}| \gt 1$