Since $\underset{n\to \infty }{lim}{e}^{-n} n\=\infty$, by the nth-term test, the given series must diverge because $a_n\=e^{-n} n\!$ does not tend to zero as $n\to \infty$.

The following two Maple calculations determine the divergence of the given series. In the first, Maple sums the series and obtains infinity as the result. In the second, Maple shows that the nth-term does not approach zero as $n\to \infty$. Either of these results suffices to establish the divergence of the series, although the first is not as convincing as the second because the Maple process behind the summation of the series is not exposed to inspection.