Suppose that f(x) is positive, continuous, decreasing function on the interval [N, ). Let a n = f(n). ThenNote that this test is much different from all the others. We have not yet formally introduced the concept of an Integral - or even of a continuous function - so that we can not prove this test here. However, for completeness it is included as a test that is sometimes useful to apply.
converges if and only if converges