Alternating series test for convergence

Definition

The alternating series test is a method used to determine if an infinite series converges or diverges. It states that if the terms of an alternating series decrease in magnitude and approach zero, then the series converges.

Related terms

Convergence:

A sequence or series is said to converge if its terms approach a finite limit as the index increases.

Divergence:

A sequence or series is said to diverge if its terms do not approach a finite limit as the index increases.

Absolute Convergence: A series is absolutely convergent if the sum of the absolute values of its terms converges.