Branches History Index

◀ ▲ ▶Branches / Analysis / Lemma: Convergence Test for Telescoping Series

Lemma: Convergence Test for Telescoping Series

Let $(b_k)_{k\in\mathbb N}$ be a convergent sequence. Then the telescoping series $\sum_{k=0}^\infty (b_k-b_{k+1})$ is a convergent series. In the case $(b_k)_{k\in\mathbb N}$ is monotonic, the series is absolutely convergent.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3

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

Github:
bookofproofs

References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
  2. Heuser Harro: "Lehrbuch der Analysis, Teil 1", B.G. Teubner Stuttgart, 1994, 11th Edition