On certain transformations of series. (English. Russian original) Zbl 0571.40001

Sov. Math. 28, No. 11, 41-48 (1984); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1984, No. 11(270), 34-40 (1984).
The author presents two rather simple transformations of convergent series that, at least in his illustrative examples, accelerate their convergence. The less complicated transformation says that if \(\lambda\) \(\neq 1\) then \(\Sigma_ 1^{\infty}a_ n=(1-\lambda)\{a_ 1+\Sigma_ 1^{\infty}(a_{n+1}-\lambda a_ n)\).
Reviewer: R.P.Boas


40A05 Convergence and divergence of series and sequences
65B99 Acceleration of convergence in numerical analysis