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Expressing e in Some New Different Ways and Developing the Sums of Infinitely Many Infinite Series

16 March 2022, Version 1
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

In this article we have expressed Euler’s number (e) in some different ways. These expressions help us to observe ‘e’ from a new perspective. In the main part of this article we have developed a formula to calculate the sum of infinitely many infinite series. Then we have shown thirteen important summations where we have added infinitely many convergent infinite series.

Keywords

Euler’s number
mathematical constant e
infinite series
summations
unconditionally convergent
rearrangement theorem

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Version History

Mar 16, 2022 Version 1

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The content is available under CC BY 4.0 [opens in a new tab]

DOI

10.33774/coe-2022-rsxrk
D O I: 10.33774/coe-2022-rsxrk [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) have declared ethics committee/IRB approval is not relevant to this content

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