Geometric Series Test

Definition

The Geometric Series Test is a method used to determine whether an infinite geometric series converges or diverges based on the common ratio (r) of the terms. If the absolute value of r is less than 1, the series converges; otherwise, it diverges.

Related terms

Ratio test: A test used to determine whether an infinite series converges or diverges based on the ratio between consecutive terms.

Divergence test: A test used to determine if an infinite series necessarily diverges by checking if its terms do not converge to zero.

Convergence:

The behavior of a sequence or series whose values approach a specific finite number as more terms are added.