English Title

On the summation of series, in which the signs of the terms alternate

Authors

Leonhard Euler

Enestrom Number

617

Fuss Index

180

Original Language

Latin

Published as

Journal article

Published Date

1788

Written Date

1776

Content Summary

This work, along with E55 and E352, examines the formal series f(a) – f(a+h) + f(a+2h) – f(a+3h) + f(a+4h) – .... Here, uses a power series, f(0) + f(1)x + f(2)x2 + f(3)x3 + ..., which is obviously what he’s looking for in the case a=0, h=1, and x=-1. He does Taylor series expansions at every value 0, 1, 2,..., sums them all, and combines terms; he gets an answer that reminds Faber of E352.

Original Source Citation

Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 2, pp. 46-69.

Opera Omnia Citation

Series 1, Volume 16A, pp.47-78.

Record Created

2018-09-25

Included in

Mathematics Commons

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