IJPAM: Volume 55, No. 3 (2009)

ON REPRESENTATION OF CERTAIN REAL NUMBERS
USING COMBINATORIAL IDENTITIES

George Grossman$^1$, Akalu Tefera$^2$, Aklilu Zeleke$^3$
$^1$Department of Mathematics
Central Michigan University
Mount Pleasant, MI 48859, USA
e-mail: gross1gw@cmich.edu
$^2$Department of Mathematics
Grand Valley State University
Allendale, MI 49401, USA
e-mail: teferaa@gvsu.edu
$^3$Department of Statistics and Probability
Lyman Briggs College
Michigan State University
East Lansing, MI 48824, USA
e-mail: zeleke@stt.msu.edu


Abstract.In this paper we present identities used to represent real numbers of the form $a\,b^{n} + c$ for appropriately chosen real numbers $a$, $b$, $c$, and non-negative integers $n$. Multiple forms of these identities using single and triple sums will be presented.

Received: August 4, 2009

AMS Subject Classification: 05A19

Key Words and Phrases: generalized Fibonacci polynomials, combinatorial identities, recurrence relations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 3