Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 284261, 11 pages
http://dx.doi.org/10.1155/2011/284261
Research Article

Some Finite Sums Involving Generalized Fibonacci and Lucas Numbers

E. Kılıç,1 N. Ömür,2 and Y. T. Ulutaş2

1Mathematics Department, TOBB University of Economics and Technology , Sogutozu, 06560 Ankara, Turkey
2Mathematics Department, Kocaeli University, 41380 İzmit Kocaeli, Turkey

Received 11 August 2011; Accepted 7 September 2011

Academic Editor: Gerald Teschl

Copyright © 2011 E. Kılıç 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.

Abstract

By considering Melham's sums (Melham, 2004), we compute various more general nonalternating sums, alternating sums, and sums that alternate according to ( − 1 ) 2 𝑛 + 1 involving the generalized Fibonacci and Lucas numbers.