Sums of reciprocals of integers

Simon Davis
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 1, Pages 1—7
DOI: 10.7546/nntdm.2019.25.1.1-7
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Simon Davis
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La Jolla, CA 92039, United States


The sums of reciprocals are demonstrated to diverge for infinite sequences consisting of arbitrarily long arithmetic progressions. It is demonstrated that there may exist sequences that do not include arithmetic progressions of arbitrary length that yield divergent sums.


  • Arithmetic sequences
  • Length
  • Divergent sums

2010 Mathematics Subject Classification

  • 11B05
  • 11B25
  • 11P21
  • 11Y55


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Cite this paper

Davis, S. (2019). Sums of reciprocals of integers. Notes on Number Theory and Discrete Mathematics, 25(1), 1-7, doi: 10.7546/nntdm.2019.25.1.1-7.

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