International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2006 / Article

Open Access

Volume 2006 |Article ID 053408 | https://doi.org/10.1155/IJMMS/2006/53408

Elom K. Abalo, Kokou Y. Abalo, "Convergence of p-series revisited with applications", International Journal of Mathematics and Mathematical Sciences, vol. 2006, Article ID 053408, 8 pages, 2006. https://doi.org/10.1155/IJMMS/2006/53408

Convergence of p-series revisited with applications

Received18 Jan 2006
Revised02 May 2006
Accepted07 May 2006
Published22 Jun 2006

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 k2. Some numerical examples are given.

References

  1. T. Cohen and W. J. Knight, “Convergence and divergence of n=11np,” Mathematics Magazine, vol. 52, p. 178, 1979. View at: Google Scholar
  2. Y. Hansheng and B. Lu, “Another proof for the p-series test,” The College Mathematics Journal, vol. 36, pp. 235–237, 2005. View at: Google Scholar
  3. D. Hughes-Hallett, A. M. Gleason, D. E. Flath et al., Calculus: Single Variable, John Wiley & Sons, New York, 3rd edition, 2002. View at: Google Scholar
  4. J. Stewart, Calculus: Early Transcendentals, Brooks/Cole, California, 5th edition, 2003. View at: Google Scholar

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.


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