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Explaining Kummer's test
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2015 (English)Manuscript (preprint) (Other academic)
Abstract [en]

Mathematical theorems and their proofs are often described as being beautyful, natural or explanatory. This paper treats the last case  and discusses explanatory versus non explanatory proofs using  a convergence theorem for positive series due to Kummer, called Kummer's test. This example was studied by Pringsheim already in the beginning in the last century and has recently been discussed by Hafner and Mancuso in relation to Steiner's criteria for an explanatory proof. We provide a mathematical analysis of Kummer's test and give a proof that we claim is explanatory in this sense. Besides this we answer a number of questions that are frequently asked about the test.

Place, publisher, year, edition, pages
Keyword [en]
Positive series, convergence, convergence test, Kummer's test, explanatory proof
National Category
Mathematical Analysis
Research subject
URN: urn:nbn:se:umu:diva-104407OAI: diva2:819461
Available from: 2015-06-10 Created: 2015-06-10 Last updated: 2015-07-01Bibliographically approved

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Sjödin, Tord
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Department of Mathematics and Mathematical Statistics
Mathematical Analysis

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