Ratio Test for Convergence

Definition

The ratio test is used to determine whether an infinite series converges or diverges by examining the limit of the ratio between consecutive terms. If this limit is less than 1, then the series converges; if it's greater than 1, then it diverges; and if it's equal to 1, further tests are needed.

Related terms

Geometric Series:

A geometric series is formed by adding together consecutive terms in which each term can be obtained by multiplying the previous term by a constant ratio.

Convergence Test:

A convergence test is a method used to determine whether an infinite series converges or diverges based on certain properties of the series.

Power Series:

A power series is an infinite series in which each term is a polynomial function of the variable raised to a non-negative integer power.