Majorant Criterion

analysis

Definition

Majorant Criterion

Let ${\sum }_{n=0}^{\infty }{a}_n$ and ${\sum }_{n=0}^{\infty }{b}_n$ be two infinite series. If $|a_n|\le b_n$ for almost all $n$ and $\sum b_n$ is convergent, then $\sum a_n$ is absolutely convergent.

In this context, the series $\sum b_n$ is called a majorant of $\sum a_n$.

Related Concepts

• Minority Criterion: The analogous test for divergence.