Answer
The root test is inconclusive.
Work Step by Step
To apply the root test, we have
$$
L=\lim _{n \rightarrow \infty} \sqrt[n]{a_{n}}=\lim _{n \rightarrow \infty} \sqrt[n]{(1+(1/n))^{-n})}\\
=\lim _{n \rightarrow \infty} \frac{1}{(1+(1/n))}=1
$$
Hence the root test is inconclusive.
