E247 -- De seriebus divergentibus

(On divergent series)


One feature of this article is an evaluation of the hyergeometric series 1-1+2-6+24-120+720-…, by looking at the function s(x) = x - x2 + 2!x3 –3!x4 + 4!x5 – 5!x6 + .... Euler attacks by interpolation methods and seems to get the answer around 0.59. Then he integrates it and evaluates again by continued fractions, and gets 0.5963473621372.

According to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on October 27, 1746.

According to the records, it was presented to the St. Petersburg Academy on March 12, 1753.

Publication: Documents Available:

Return to the Euler Archive