In mathematics, the ratio test is a test (or "criterion") for the convergence of a series
∑
n
=
1
∞
a
n
,
{\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.