A Method for Accelerating of Convergence of Numerical and Power Series

In this paper is examined the acceleration of convergence of alternative and non-alternative numerical and power series by means of an Euler-Abel type operator, that is defined earlier by G.A.Sorokin and I.Z.Milovanovic. Through this type of linear operator of generalized difference of sequence is achieved that alternative and non-alternative numerical and power series to be transformed into series with higher speed of convergence than the initial series. At the end of this paper is given the implementation of this method through a numeric example.