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 an is convergent if there exists a monotonically decreasing function ƒ such that ƒ(n) = an 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.