I ended up having the infinite product
$$ A=\prod_{n=1}^{\infty}(1+a_n) $$
for $a_n$ a positive series. What I would like to do is show that this is convergent. On the other hand I have the sum
$$ B=\sum_{n=1}^{\infty}a_n $$
Is it true that $A$ and $B$ both converge or both diverge? Thanks