English Title
Universal method for summation of series, further developed
Enestrom Number
55
Fuss Index
177
Original Language
Latin
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.
Published as
Journal article
Published Date
1741
Written Date
1736
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
