E55 -- Methodus universalis series summandi ulterius promota

(Universal method for summation of series, further developed)


This, along with E617, 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 E617. 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 and gets an answer that reminds Faber of E352.

According to the records, it was presented to the St. Petersburg Academy on September 17, 1736.

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