1. A series is absolutely convergent if the limit as n approaches infinity of its nth term raised to the 1/n power is less than unity.

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