Terminal Summation: Extending the Concept of Convergence

Authors

Max Tran, CUNY Kingsborough Community CollegeFollow
Ayalur Krishnan

Document Type

Article

Publication Date

2014

Abstract

This paper presents an atypical method for summing divergent series, and provides a sum for the divergent series log(n). We use an idea of T.E. Phipps, called Terminal Summation, which uses asymptotic analysis to assign a value to divergent series. The method associates a series to an appropriate difference equations having boundary conditions at infinity, and solves the difference equations which then provide a value for the original series. We point out connections between Phipps' method, the Euler-MacLaurin sum formula, the Ramanujan sum and other traditional methods for summing divergent series.

Comments

This article was originally published in The Journal of Global Research in Mathematical Archives.

It is distributed under the terms of a Creative Commons Attribution-NonCommercial-ShareAlike license (CC BY-NC-SA).