Let $\{X_n, F_n\}_{n\geq0}$ be a martingale.
We know that $EX^2_n < \infty$ and $\sum_{n=1}^\infty \frac {E(X_n - X_{n-1})^2}{n^2} < \infty$
Prove that $\frac {X_n}{n} \rightarrow 0$ almost certainly and $E(\frac{X_n}{n})^2 \rightarrow 0$.
It can be shown that by the martingale property $E(X_n - X_{n-1})^2 = E(X_n)^2 - E(X_{n-1})^2$ but I'm not sure where to go from here, or if its even a correct first step.