International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 78739, 8 pages

Summation identities for representation of certain real numbers

George Grossman,1 Akalu Tefera,2 and Aklilu Zeleke3,4

1Department of Mathematics, Central Michigan University, Mount Pleasant 48859, MI, USA
2Department of Mathematics, Grand Valley State University, Allendale 49401, MI, USA
3Lyman Briggs School, Michigan State University, East Lansing 48825-1107, MI, USA
4Department of Statistics and Probability, Michigan State University, East Lansing 48824-1027, MI, USA

Received 27 March 2006; Accepted 28 March 2006

Copyright © 2006 George Grossman et al. 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 present identities used to represent real numbers of the form xum±yvn for appropriately chosen real numbers x, y, u, v and nonnegative integers m and n. We present the proofs of the identities by applying Zeilberger's algorithm.