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