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 as n approaches infinity of its n th term raised to the 1/ n power is less than unity.

A series a_n is convergent if there exists a monotonically decreasing function ƒ such that ƒ(n) = a_n for n greater than some fixed number N, and if the integral of ƒ(x) dx from N to ∞ converges. Also known as Cauchy integral test; Maclaurin-Cauchy test.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.