So, there is a sequence of identically distributed independent random variables taking values on the integers, and they have a positive expectation. The problem is to prove that with probability 1 the sum from 1 to k of the random variables is 0 for finitely many k.
I was thinking to use the first Borel Cantelli Lemma, but I can't seem to show that the sum of the probabilities is finite.
Thanks in advance!