A generalized alternating harmonic series

Shelby Kilmer; Songfeng Zheng; Shelby Kilmer; Songfeng Zheng

doi:10.3934/math.2021781

AIMS Mathematics

2021, Volume 6, Issue 12: 13480-13487. doi: 10.3934/math.2021781

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Research article

A generalized alternating harmonic series

Shelby Kilmer ^,,
Songfeng Zheng

Department of Mathematics, Missouri State University, 901 S. National, Springfield, MO 65897, USA

Received: 30 July 2021 Accepted: 13 September 2021 Published: 18 September 2021
MSC : 40A05, 11A99

This paper introduces a generalization of the alternating harmonic series, expresses the sum in two closed forms, and examines the relationship between these sums and the harmonic numbers.
- alternating harmonic series,
- sum of infinite series,
- rearrangement of series,
- harmonic numbers
Citation: Shelby Kilmer, Songfeng Zheng. A generalized alternating harmonic series[J]. AIMS Mathematics, 2021, 6(12): 13480-13487. doi: 10.3934/math.2021781

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Abstract

This paper introduces a generalization of the alternating harmonic series, expresses the sum in two closed forms, and examines the relationship between these sums and the harmonic numbers.

References

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