$\mathbb{P}[X_{n}$ is head $] = p_{n}$.
$F$ is the event that only finitely many heads are observed.
How do I prove $\mathbb{P}[F]=1$ iff $\sum_{n=1}^{\infty} p_{n} <\infty$
I am confused about this question from my text book. How do I go about doing this proof.
It seems obvious to me that if there are finitely many heads then their probabilities for each one is a finite number?
Please could I have help and not the full answer. Thanks!
I assume it has something to do with the Borel-Cantelli Lemma