Answer
converges absolutely
Work Step by Step
Let us consider $a_n=(-1)^{n+1}(0.1)^n$ and $u_n$ refers to the all positive values of $n$.
Also, $|a_n|=(0.1)^n$
This implies that the series $\Sigma_{n=1}^\infty |u_n| $ shows a convergent geometric series and having common ratio $r=0.1$.
Hence, the given series converges absolutely.