Hello,

You have to think of Borel-Cantelli's lemma !

Let (we know it's impossible for to equal 0).

We want to prove that almost surely, An happens a finite number of times, that is to say not an infinite number of times. So that is

So we just have to prove that , which is easy since there are n Xi's equal to -1 and n equal to 1.

So .

So .

Hence the result.