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Integral test

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2020 Mathematics Subject Classification: Primary: 40A05 [MSN][ZBL]

An elementary criterion for the convergence of the series $\sum_n f(n)$ when $f:[1, \infty[\to [0, \infty[$ is a monotone decreasing function: the series converges if and only if the integral \[ \int_1^\infty f(x)\, dx \] is finite.

How to Cite This Entry:
Integral test. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Integral_test&oldid=30932