A Dilution Test for the Convergence of Subseries of a Monotone Series

Details A Dilution Test for the Convergence of Subseries of a Monotone Series A Dilution Test for the Convergence of Subseries of a Monotone Series

2010-11-17

arxiv.org/abs/1011.4697v1

Journal of Classical Analysis, Volume 1, Number 1 (2012), 17-22

Mathematics

Classical Analysis and ODEs

5 pages, 1 figure

Scientific paper

Cauchy's condensation test allows to determine the convergence of a monotone series by looking at a weighted subseries that only involves terms of the original series indexed by the powers of two. It is natural to ask whether the converse is also true: Is it possible to determine the convergence of an arbitrary subseries of a monotone series by looking at a suitably weighted version of the original series? In this note we show that the answer is affirmative and introduce a new convergence test particularly designed for this purpose.

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