What is ratio test convergence?

The ratio test is a mathematical test used to determine the convergence or divergence of an infinite series. It states that for a series ∑an, if the limit of the absolute value of the ratio of consecutive terms |an+1/an| as n approaches infinity is less than 1, then the series converges. If the limit is greater than 1 or does not exist, then the series diverges. If the limit is equal to 1, the test is inconclusive and other tests may need to be used.

The ratio test is particularly useful for series with factorials, exponential functions, or powers of n in the terms. It is often used in calculus and advanced calculus courses to determine whether a series converges or diverges. It is important to note that the ratio test does not provide information about the sum of a convergent series, just about its convergence or divergence.