A dilution test for the convergence of subseries of a monotone series

Lasse Leskelä, Mikko Stenlund

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)17-22
Number of pages6
JournalJOURNAL OF CLASSICAL ANALYSIS
Volume1
Issue number1
Publication statusPublished - 2012
MoE publication typeA1 Journal article-refereed

Fingerprint Dive into the research topics of 'A dilution test for the convergence of subseries of a monotone series'. Together they form a unique fingerprint.

Cite this