Explaining Kummer's test
2015 (English)Manuscript (preprint) (Other academic)
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
Positive series, convergence, convergence test, Kummer's test, explanatory proof
Research subject Mathematics
IdentifiersURN: urn:nbn:se:umu:diva-104407OAI: oai:DiVA.org:umu-104407DiVA: diva2:819461