So SLLN holds and mean of the independent random variables $xi$ is 0, I have to prove that the series of $\frac{\xi_n}{n^{1+\alpha}}$ converges for any $\alpha > 0$.
I'm using 3-series theorem but not sure how to use SLLN to prove that the series $\operatorname{Var} \left( \frac{\xi_n}{n^{1+\alpha}} \right)$ converges. I'd greatly appreciate your help.