Universal method of accurately finding sums of convergent series
This paper begins with an expression of the trapezoid rule for "formal mechanical quadrature." Euler also sums the first ten terms of ζ(2) to get 1.549768 and gives an expression for the error term. Then he determines the sum of the first million terms of the harmonic series to be 14.392669.
Original Source Citation
Commentarii academiae scientiarum Petropolitanae, Volume 8, pp. 3-9.
Opera Omnia Citation
Series 1, Volume 14, pp.101-107.