Ratio Test
The Ratio Test is a mathematical convergence test used in calculus and analysis to determine whether an infinite series converges or diverges. It involves computing the limit of the absolute value of the ratio of successive terms in the series. If this limit is less than 1, the series converges absolutely; if greater than 1, it diverges; and if equal to 1, the test is inconclusive.
Developers should learn the Ratio Test when working with algorithms, numerical methods, or data analysis that involve series approximations, such as in machine learning for gradient descent convergence or in scientific computing for evaluating infinite sums. It is particularly useful for power series and series with factorial or exponential terms, helping ensure computational stability and accuracy in iterative processes.