Terminal Summation: Extending the concept of convergence

Main Article Content

Max Tran

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.

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How to Cite
Tran, M. (2014). Terminal Summation: Extending the concept of convergence. Journal of Global Research in Mathematical Archives(JGRMA), 2(2), 44–52. Retrieved from https://jgrma.com/index.php/jgrma/article/view/152
Section
Mathematical Section
Author Biography

Max Tran, Kingsborough Community College

Assistant Professor in the Department of Mathematics and Computer Science

References

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