I am trying to prove the following:

.

Here's what I have so far:

FTSOC assume . We know that and for only finitely many . Then for only finitely many . This implies almost always. So, almost always.

But this doesn't get me anywhere. Where am I going wrong? If I let , I just get . So, this tells me nothing.

Any help would be appreciated. (Even though it doesn't state it, I am assuming that all are nonnegative.)