# Ratio test

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

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

where each term is a real or complex number and an is nonzero when n is large. 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.[1]