Ratio test

In mathematics, the ratio test is a test (or 'criterion') for the convergence of a series L = lim n → ∞ | a n + 1 a n | . {displaystyle L=lim _{n o infty }left|{frac {a_{n+1}}{a_{n}}} ight|.}     (1) In mathematics, the ratio test is a test (or 'criterion') for the convergence of a series 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. The usual form of the test makes use of the limit