On two conjectures concerning the partial sums of the harmonic series

Stephen M. Zemyan

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let Sn denote the nth partial sum of the harmonic series. For a given positive integer k>1, there exists a unique integer nk such that Snk-1<Snk. It has been conjectured that nki is equal to the integer nearest ek-γ, where γ is Euler's constant. We provide an estimate on nk which suggests that this conjecture may have to be modified. We also propose a conjecture concerning the amount by which Snk- and Snk differ from k.

Original languageEnglish (US)
Pages (from-to)83-86
Number of pages4
JournalProceedings of the American Mathematical Society
Volume95
Issue number1
DOIs
StatePublished - Sep 1985

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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