The Integral test for convergence reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Integral test for convergence

The integral test for convergence is a method used to test infinite series of nonnegative terms for convergence.

The series

converges if and only if the integral

is finite, where f(x) is a positive monotone decreasing function defined on the interval [1, ∞) and f(n) = a_n for all n.

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