# convergence criterion for infinite product

Let $\prod_{n=1}^{\infty}p_{n}$ be an infinite product. We have the following:

• $\prod_{n=1}^{\infty}p_{n}$ is convergent iff $\sum_{n=1}^{\infty}\ln{p_{n}}$ is convergent.

• $\prod_{n=1}^{\infty}(1+p_{n})$ is convergent iff $\sum_{n=1}^{\infty}p_{n}$ converges absolutely.

Title convergence criterion for infinite product ConvergenceCriterionForInfiniteProduct 2013-03-22 14:50:07 2013-03-22 14:50:07 aplant (12431) aplant (12431) 7 aplant (12431) Theorem msc 30E20