Answer
Converges
Work Step by Step
Consider $u_n=(-1)^{n+1}\dfrac{(0.1)^n}{n}$
Here, $u_n$ is positive for all the values of $n$.
and $|u_n|=\dfrac{(0.1)^n}{n}\lt (0.1)^n$
We know that $(0.1)^n$ describes a convergent geometric series.
Thus the series converges absolutely by the Direct Comparison Test.