by **Daniel** » Tue Aug 02, 2011 10:25 pm

I know this topic is pretty old now but i've been using this book as self study before my final year as an undergrad so just thought I would try and outline the approach I was going to try and would like to know if you felt I was heading down the right track..

If S:= Sum{p_n} < infinity, then there is N s.t. S_N := Sum_{n>N}(p_n) -> 0. Then the Prod_{n>N}(1-p_n) >= 1 - S_ N and taking limits would suggest Prod_{n>N}(1-p_n) -> 1.

Then Prod(1-p_n) = Prod_{1<=n<=N}(1-p_n) * Prod_{n>N}(1-p_n) and using the result above suggests this tends towards Prod_{1<=n<=N} (1-p_n). And since the product is now finite and each (1-p_n) > 0 we have Prod(1-p_n) > 0.