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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 53408, 8 pages

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 Hindawi Publishing Corporation. 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.


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 k2. Some numerical examples are given.