$\frac{S_n}{n} \to -1 \ \ a.e.$, exercise from probability book I'm stuck with this exercise from Williams, probability with martingales. 
Let $X_1, X_2, \ldots $be independent random variables with $$P(X_n = n^2-1 )= \frac{1}{n^2}$$  $$P(X_n = -1 )= 1-\frac{1}{n^2}$$
Then if $S_n = X_1+ X_2, + \ldots + X_n$ we have $$\frac{S_n}{n} \to -1 \ \ a.e.$$
Any hint ?

Hint: Since $$\sum_{n \geq 1} \mathbb{P}(X_n \neq -1) < \infty$$ it follows from the Borel-Cantelli lemma that for almost all $\omega \in \Omega$ there exists $N = N(\omega)$ such that $$X_n(\omega)=-1 \qquad \text{for all} \, n \geq N.$$
