A remarkable formula for approximating the sum of alternating series
Thomas J. Osler · The Mathematical Gazette · 2009
In this paper we present a simple formula that can often be used to assist in the approximation of the sum of an alternating seriesThe ideas presented here were motivated by translating Euler's papers [1] and [2]. Suppose we begin by summing a terms of this series exactly, then the approximation that we will obtain is given by