International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 53408, 8 pages
doi:10.1155/IJMMS/2006/53408
Convergence of p-series revisited with applications
1Departments of Physics; Departments of Mathematics, Wofford College, Spartanburg 29303, SC, USA
2Department of Mathematics, Erskine College, Due West 29639, SC, USA
Received 18 January 2006; Revised 2 May 2006; Accepted 7 May 2006
Copyright © 2006 Elom K. Abalo and Kokou Y. Abalo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.