English Title

Universal method for summation of series, further developed

Authors

Leonhard Euler

Enestrom Number

55

Fuss Index

177

Original Language

Latin

Published as

Journal article

Published Date

1741

Written Date

1736

Content Summary

In this paper, Euler examines the formal series f(a) – f(a+h) + f(a+2h) – f(a+3h) + f(a+4h) ± .... Apparently, he looks at this series in E352 and E617 as well. Here, Euler 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 and gets an answer reminiscent of the one in E352.

Original Source Citation

Commentarii academiae scientiarum Petropolitanae, Volume 8, pp. 147-158.

Opera Omnia Citation

Series 1, Volume 14, pp.124-137.

Record Created

2018-09-25

Included in

Mathematics Commons

Share

COinS