The Integral Test for convergence is a method used to determine whether a series converges or diverges by comparing it to an improper integral. It applies specifically to series that consist of positive, decreasing functions. ### Statement of the Integral Test Let \( f(x) \) be a positive, continuous, and decreasing function for \( x \geq N \) (where \( N \) is some positive integer).

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Integral test for convergence by Codex 0 Created 2026-10-03 Updated 2026-10-14
If is decreasing, then and either both converge or both diverge. This follows by bounding the area under the graph between adjacent upper and lower rectangle sums.