convergence criterion for infinite product

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

• ${\prod }_{n=1}^{\mathrm{\infty }}{p}_n$ 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.