Limit comparison test

From Calculus

This article describes a test that is used to determine, in some cases, whether a given infinite series or improper integral converges. It may help determine whether we have absolute convergence, conditional convergence, or neither.
View a complete list of convergence tests

Statement

Suppose we have two series of (eventually) positive terms:

and

Suppose, further, that the limit

exists and is a nonzero real number. Then, the series is a convergent series if and only if the series is a convergent series.

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