What is ratio test calculus?

The ratio test is a method used to determine the convergence of an infinite series in calculus. This test involves taking the limit of the absolute value of the ratio of consecutive terms in the series as n approaches infinity. If the limit is less than 1, the series converges. If the limit is greater than 1 or does not exist, the series diverges. If the limit equals 1, the test is inconclusive and another test may need to be used.

The ratio test can be particularly useful when dealing with series that involve factorials or exponentials. It is a powerful tool for determining convergence or divergence, but it may not always provide a definitive answer. In such cases, it is important to consider using other convergence tests to further analyze the series.

In summary, the ratio test in calculus is a method used to determine whether an infinite series converges or diverges by taking the limit of the ratio of consecutive terms as n approaches infinity.