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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## Details

### Authors and affiliations

Simon Davis

*8861 Villa La Jolla Drive #13595
La Jolla, CA 92039, United States
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### Abstract

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.

### Keywords

- Arithmetic sequences
- Length
- Divergent sums

### 2010 Mathematics Subject Classification

- 11B05
- 11B25
- 11P21
- 11Y55

### References

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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.