The limit comparison test is a method for determining whether a series converges or diverges by comparing it to another series with known behavior. It is especially useful when the terms of the series are not easily bounded.

Formally, it can be defined as:

Let and be two series with and for all sufficiently large. Suppose that the limit exists and then converges if and only if converges, and diverges if and only if diverges.

In essence, if the ratio of the terms approaches a finite, positive constant, then the two series share the same vergence behavior.