6533b7dcfe1ef96bd12733ed
RESEARCH PRODUCT
A dilution test for the convergence of subseries of a monotone series
Lasse LeskeläMikko Stenlundsubject
Monotone polygonSeries (mathematics)Mathematics - Classical Analysis and ODEsConvergence (routing)ConverseClassical Analysis and ODEs (math.CA)FOS: MathematicsApplied mathematicsCauchy distributionGeneral MedicineMathematicsTest (assessment)description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-11-17 | Journal of Classical Analysis |