Infinite Families of Infinite Series With Integer Sums

Damiano Fulghesu; James A. Sellers; Courtney K. Taylor

doi:10.1080/07468342.2022.2160611

Infinite Families of Infinite Series With Integer Sums

Damiano Fulghesu, James A. Sellers, Courtney K. Taylor

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Summary: Motivated by a desire to show first-year calculus students examples of infinite series whose sums are relatively straightforward to find, we demonstrate a technique to calculate such sums using tools often demonstrated to calculus students. We then use these results, which include an explicit formula for the sums in question, to prove the existence of an infinite family of infinite series whose sums are integers.

Original language	English (US)
Pages (from-to)	33-43
Number of pages	11
Journal	College Mathematics Journal
Volume	54
Issue number	1
DOIs	https://doi.org/10.1080/07468342.2022.2160611
State	Published - 2023

Bibliographical note

Funding Information:
During the development of this work, Damiano Fulghesu was partially supported by Simons collaboration grant 36031.

Publisher Copyright:
© 2023 The Mathematical Association of America.

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10.1080/07468342.2022.2160611

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N2 - Summary: Motivated by a desire to show first-year calculus students examples of infinite series whose sums are relatively straightforward to find, we demonstrate a technique to calculate such sums using tools often demonstrated to calculus students. We then use these results, which include an explicit formula for the sums in question, to prove the existence of an infinite family of infinite series whose sums are integers.

AB - Summary: Motivated by a desire to show first-year calculus students examples of infinite series whose sums are relatively straightforward to find, we demonstrate a technique to calculate such sums using tools often demonstrated to calculus students. We then use these results, which include an explicit formula for the sums in question, to prove the existence of an infinite family of infinite series whose sums are integers.

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Infinite Families of Infinite Series With Integer Sums

Abstract

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