Showing that $Y := |\sum_{n\geq1}X_n|$ converges with Borel-Cantelli lemmas

Question

Let $(X_n)_{n\geq1}$ a sequence of i.i.d rv's with distribution $P(X_n=\frac{1}{n})=P(X_n=-\frac{1} {n})=\frac{1}{2}$ We need to show that $Y := |\sum_{n\geq1}X_n|$ converges a.s. It is also noted that $E[|Z|]\leq E[Z^2]^\frac{1}{2}$ might be usefull. How do we use the Borel-Contelli lemma's to show this?