E46 -- Methodus universalis serierum convergentium summas quam proxime inveniendi

(Universal methods of series)


This paper begins with an expression of the trapezoid rule for "formal mechanical quadrature." Euler evaluates the first ten terms of z(2) to be 1.549768 (probably in his head) and gives an expression for the error term. Then he finds the sum of the first million terms of the harmonic series to be 14.392669.

According to the records, it was presented to the St. Petersburg Academy on June 9, 1735.

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