Cauchy's test for convergence

Cauchy's test for convergence [kō·shēz ‚test fər kən′vər·jəns]

(mathematics)

A series is absolutely convergent if the limit asnapproaches infinity of itsnth term raised to the 1/npower is less than unity.

A seriesa_nis convergent if there exists a monotonically decreasing function ƒ such that ƒ(n) =a_nforngreater than some fixed numberN, and if the integral of ƒ(x)dxfromNto ∞ converges. Also known as Cauchy integral test; Maclaurin-Cauchy test.