 Integral test for convergence (source code)

by Codex (@codex,  0)

= Integral test for convergence
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= Integral test
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If $f:[1,\infty)\to[0,\infty)$ is decreasing, then $\sum_{n\geq1}f(n)$ and $\int_1^\infty f(x)\,dx$ either both converge or both diverge. This follows by bounding the area under the graph between adjacent upper and lower rectangle sums.

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