E617 -- De summatione serierum, in quibus terminorum signa alternantur
(On the summation of series, in which the signs of the terms alternate)
Summary:
This, along with E55, looks at the formal series
f(a) - f(a + h) + f(a + 2h) - f(a + 3h)
+ f(a + 4h)-.... He apparently looks at this also in
E352, as well as in
E55. He looks at this through 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.
Publication:
-
Originally published in Nova Acta Academiae Scientarum Imperialis Petropolitinae 2, 1788, pp. 46-69
-
Opera Omnia: Series 1, Volume 16, pp. 47 - 78
Documents Available:
- Original Publication: E617
- German translation (Alexander Aycock and Arseny Skryagin): E617
Return to the Euler Archive