Ratio test

In mathematical analysis, the ratio test is a test (or "criterion") for the convergence of a series

$\sum _{n=1}^{\infty }a_{n},$

where each term is a real or complex number and all but finitely many terms are non-zero. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test.