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Proposition: Monotony Criterion
An infinite series \(\sum_{k=0}^\infty x_k\) with nonnegative terms \(x_k\ge 0\) for all \(k\in\mathbb N\) is convergent if and only if the sequence \((s_n)_{n\in\mathbb N}\) of its partial sums \(s_n:=\sum_{k=0}^n x_k\) is bounded.
Table of Contents
Corollaries: 1 Proofs: 1
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Proofs: 1 2
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983