Answer
Diverges
Work Step by Step
Let us consider $a_n=(-1)^{n+1}(\dfrac{n}{10})^n$and $u_n$ refers to all positive values of $n$.
Then , $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (-1)^{n+1}(\dfrac{n}{10})^n \ne 0$
Hence, the series diverges by the Nth Term Test for Divergence.