Integral test for convergence

In mathematics, the integral test for convergence is a method used to test infinite series of monotonous terms for convergence. It was developed by Colin Maclaurin and Augustin-Louis Cauchy and is sometimes known as the Maclaurin–Cauchy test.

The integral test applied to the harmonic series. Since the area under the curve y = 1/x for x[1, ∞) is infinite, the total area of the rectangles must be infinite as well.