Nth Term Test

Definition

The nth Term Test is a method used to determine whether an infinite series converges or diverges by examining the behavior of its individual terms. If the limit of the sequence of terms as n approaches infinity is not zero, then the series diverges. If the limit is zero, further tests are needed to determine convergence.

Related terms

Converges: When an infinite series converges, it means that the sum of all its terms approaches a finite value as more terms are added.

Diverges:

When an infinite series diverges, it means that the sum of its terms does not approach a finite value but instead grows infinitely larger or oscillates between different values.

Geometric Series:

A geometric series is a specific type of infinite series where each term is obtained by multiplying the previous term by a constant ratio.