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A Short and Unified Proof of Kummer's Test
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0001-8075-9129
2018 (English)Other (Other academic)
Abstract [en]

Kummer’s test from 1835 states that the positive series ∑n=1an is convergent if and only if there is a sequence {Bn}1 of positive numbers such that Bn·an/an+1Bn+1 ≥ 1, for all sufficiently large n. We present an exact analysis and a short and unified proof of Kummer’s test. The test has been applied to differential equations and studied in mathematical philosophy.

Place, publisher, year, pages
2018. , p. 4
Keywords [en]
Sequence, positive series, convergence test, mathematical explanation
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-153059OAI: oai:DiVA.org:umu-153059DiVA, id: diva2:1260825
Available from: 2018-11-05 Created: 2018-11-05 Last updated: 2018-11-09Bibliographically approved

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fulltext(105 kB)11 downloads
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Sjödin, Tord
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf