convergence criterion for infinite product
Let ${\prod}_{n=1}^{\mathrm{\infty}}{p}_{n}$ be an infinite product. We have the following:

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${\prod}_{n=1}^{\mathrm{\infty}}{p}_{n}$ is convergent^{} iff ${\sum}_{n=1}^{\mathrm{\infty}}\mathrm{ln}{p}_{n}$ is convergent.

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${\prod}_{n=1}^{\mathrm{\infty}}(1+{p}_{n})$ is convergent iff ${\sum}_{n=1}^{\mathrm{\infty}}{p}_{n}$ converges absolutely.
Title  convergence criterion for infinite product 

Canonical name  ConvergenceCriterionForInfiniteProduct 
Date of creation  20130322 14:50:07 
Last modified on  20130322 14:50:07 
Owner  aplant (12431) 
Last modified by  aplant (12431) 
Numerical id  7 
Author  aplant (12431) 
Entry type  Theorem 
Classification  msc 30E20 