Rapidly Convergent Series from Positive Term Series

Abstract

In this paper we shall give description about the extraction of a rapidly decaying remainder from Euler series and telescoping series. Then we apply the procedure to generalised telescoping series. The new positive term series obtained with rapidly decaying remainder will converge faster than the original series. We shall apply the procedure to generalised telescoping series also. The introduction of such remainder will give a better approximation for the series.