Limit comparison test

In mathematics, the limit comparison test (LCT) (in contrast with the related direct comparison test) is a method of testing for the convergence of an infinite series.

Suppose that we have two series ${\displaystyle \Sigma _{n}a_{n}}$ and ${\displaystyle \Sigma _{n}b_{n}}$ with ${\displaystyle a_{n},b_{n}\geq 0}$ for all ${\displaystyle n}$.

...
Wikipedia