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{{MSC|40A05}}
{{TEX|done}}

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.

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

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