In mathematics, the nth-term test for divergence is a simple test for the divergence of an infinite series: If or if the limit does not exist, then diverges. Many authors do not name this test or give it a shorter name. == Usage == Unlike stronger convergence tests, the term test cannot prove by itself that a series converges. In particular, the converse to the test is not true; instead all one can say is: If then may or may not converge. In other words, if the test is inconclusive. The harmonic series is a classic example of a divergent series whose terms limit to zero. The more general class...