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Definition: Rearrangement of Infinite Series

Let $\sum_{k=0}^\infty x_k$ be a real series and let $\sigma:\mathbb N\to\mathbb N$ be a permutation of its indices. Then the series

$$\sum_{k=0}^\infty x_{\sigma(k)}$$

is called the rearrangement of the original real series.

Table of Contents

1. Proposition: Rearrangement of Absolutely Convergent Series
2. Proposition: Rearrangement of Convergent Series

Mentioned in:

Proofs: 1
Propositions: 2 3

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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983