Euler summation

Summary

Euler summation is a summability method that replaces a series by a new series built from binomial combinations of its terms. The value is the sum of the new series. It goes back to the Euler transform of alternating series, which speeds up their convergence. The method gives the usual sum to every convergent series and sums many divergent alternating series. It belongs to the family of Hausdorff methods, together with the Cesàro methods.