Quotient Criterion

analysis

Definition

Quotient Criterion

The quotient criterion (or ratio test) is a convergence criterion for an infinite series :

1. If there exists such that for almost all , then the series is absolutely convergent.
2. If for almost all , then the series is divergent.

Limit Form

Using the limit superior and limit inferior:

• absolutely convergent.
• divergent.

Example

Let . We examine the ratio:

Since , the series converges.