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Proposition: Cauchy Condensation Criterion
An infinite series $\sum_{k=0}^\infty x_k$ with a monotonically decreasing real sequence $(x_k)_{k\in\mathbb N}$ of non-negative members $x_k\ge 0$ for all $k\in\mathbb N$ is convergent if and only if the "condensed series" $$\sum_{n=0}^\infty 2^n x_{2^n}$$ is convergent.
Table of Contents
Examples: 1 Proofs: 1
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Examples: 1
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References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
- Heuser Harro: "Lehrbuch der Analysis, Teil 1", B.G. Teubner Stuttgart, 1994, 11th Edition
