Minority Criterion

analysis

Definition

Minority Criterion

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

In this context, the series $\sum a_n$ is called a minority (or minorant) of $\sum b_n$.

Related Concepts

• Majorant Criterion: The analogous test for convergence.