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]

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[581] **Forster Otto**: “Analysis 1, Differential- und Integralrechnung einer VerĂ¤nderlichen”, Vieweg Studium, 1983

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