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Corollary: Monotony Criterion for Absolute Series

(related to Proposition: Monotony Criterion)

An infinite series \(\sum_{k=0}^\infty x_k\) is absolutely convergent if and only if the sequence \((s_n)_{n\in\mathbb N}\) of its partial sums of absolute terms \(s_n:=\sum_{k=0}^n |x_k|\) is bounded.

Table of Contents

Proofs: 1

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References

Bibliography

  1. Heuser Harro: "Lehrbuch der Analysis, Teil 1", B.G. Teubner Stuttgart, 1994, 11th Edition