The ratio test is a method used in calculus to determine whether an infinite series converges (adds up to a finite value) or diverges (grows without bound). It involves taking the limit of the absolute value of the ratio between consecutive terms in the series. If the limit is less than 1, the series converges; if it is greater than 1, the series diverges; and if it equals 1, the test is inconclusive.
For example, in the series 1/2 + 1/4 + 1/8 + 1/16 + …, the ratio of each term to the previous term is 1/2. Taking the limit gives a value less than 1, so the ratio test tells us that this series converges.
