International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 5, Pages 8 p.
doi:10.1155/IJMMS/2006/53408

Convergence of p-series revisited with applications

Elom K. Abalo1 and Kokou Y. Abalo2

1Departments of Physics
 2Departments of Mathematics, Wofford College, Spartanburg 29303, SC, USA
 3Department of Mathematics, Erskine College, Due West 29639, SC, USA

Abstract

We construct two adjacent sequences that converge to the sum of a given convergent p-series. In case of a divergent p-series, lower and upper bounds of the (kn)th partial sum are constructed. In either case, we extend the results obtained by Hansheng and Lu (2005) to any integer k≥2. Some numerical examples are given.