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 hes 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.

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