convergence criterion for infinite product

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

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

• ${\prod }_{n=1}^{\mathrm{\infty }}(1+p_n)$ is convergent iff ${\sum }_{n=1}^{\mathrm{\infty }}{p}_n$ converges absolutely.

Title	convergence criterion for infinite product
Canonical name	ConvergenceCriterionForInfiniteProduct
Date of creation	2013-03-22 14:50:07
Last modified on	2013-03-22 14:50:07
Owner	aplant (12431)
Last modified by	aplant (12431)
Numerical id	7
Author	aplant (12431)
Entry type	Theorem
Classification	msc 30E20