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Proposition: Integral Test for Convergence
Let $N\in\mathbb N$ be a non-negativ natural number ($N\ge 1$) and let $f:[N,\infty)\to\mathbb R_+$ be a monotonically decreasing and non-negative-valued function. The infinite series $$\sum_{n=N}^\infty f(n)$$ is convergent if and only if the improper integral.
$$\int_{N}^\infty f(n)dx$$
is convergent.
Table of Contents
Proofs: 1
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References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
