Let $(X\_n)\_{n\geq 1}$ be independent random variables with expected value $m$ and $\sup\_n Var(X\_n)\leq K < \infty$, and they are uncorrelated. 

Then 

$1)$ $$\sum\_{i=1}^n \frac{X\_i}{n} $$ converges to $m$ in $L^2$.

$2)$ $$\sum\_{i=1}^{n^2} \frac{X\_i}{n^2}$$ converges to $m$ almost everywhere.

I have done point $1$ but I'm stuck with point $2$, how to proceed ?