Answer
Diverges
Work Step by Step
Consider $u_n=(-1)^{n+1}(\dfrac{n}{10})^n$
Here, $u_n$ is positive for all the values of $n$.
Now $\lim\limits_{n \to \infty} (\dfrac{n}{10})^n\ne 0$
Hence, the series diverges by the nth Term Test for Divergence.