Answer
Inconclusive
Work Step by Step
Apply the root test:
Therefore, $ L=\lim\limits_{k \to \infty} |a_k|^{1/k}=\lim\limits_{k \to \infty} |(1-e^{-k})^k|^{1/k}\\=\lim\limits_{k \to \infty} 1-e^{-k}\\=1-0 \\=1$
So, we can conclude that the given series is inconclusive by the root test.