Ratio test

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

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

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${\displaystyle f(a)-f(b)=\int _{b}^{a}f'(t)\,dt}$
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where each term is a real or complex number and a_n 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.