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The American Mathematical Monthly Volume 125, 2018 - Issue 4
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Notes

Subsums of the Harmonic Series

Brian LubeckSan Diego State University, 5500 Campanile Dr., San Diego, [email protected]
&
Vadim PonomarenkoSan Diego State University, 5500 Campanile Dr., San Diego, [email protected]
Pages 351-355 | Published online: 22 Mar 2018
 
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Abstract

We consider subsums of the harmonic series, and determine conditions for their convergence. We apply these conditions to determine convergence for a family of series that generalizes Kempner’s series.

ACKNOWLEDGMENT

The authors would like to thank the anonymous referees for many helpful suggestions, and for the elementary proof of Theorem 2.

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