◀ ▲ ▶Branches / Analysis / Definition: Rearrangement of Infinite Series

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

Thank you to the contributors under CC BY-SA 4.0!

Github:

References

Bibliography

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