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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.

| | | | | created: 2020-02-09 13:51:09 | modified: 2020-02-09 13:52:25 | by: bookofproofs | references: [581], [586]

1.Proof: (related to "Convergence Test for Telescoping Series")

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Bibliography (further reading)

[581] Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983

[586] Heuser Harro: “Lehrbuch der Analysis, Teil 1”, B.G. Teubner Stuttgart, 1994, 11. Auflage