Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 684280, 7 pages
http://dx.doi.org/10.1155/2012/684280
Research Article

On Reciprocal Series of Generalized Fibonacci Numbers with Subscripts in Arithmetic Progression

Neşe Ömür

Department of Mathematics, Kocaeli University, 41380 Izmit, Turkey

Received 24 October 2011; Accepted 16 November 2011

Academic Editor: Elena Braverman

Copyright © 2012 Neşe Ömür. 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

We investigate formulas for closely related series of the forms: ∑ ∞ 𝑛 = 0 1 / ( 𝑈 𝑎 𝑛 + 𝑏 + 𝑐 ) , ∑ ∞ 𝑛 = 0 ( − 1 ) 𝑛 𝑈 𝑎 𝑛 + 𝑏 / ( 𝑈 𝑎 𝑛 + 𝑏 + 𝑐 ) 2 , ∑ ∞ 𝑛 = 0 𝑈 2 ( 𝑎 𝑛 + 𝑏 ) / ( 𝑈 2 𝑎 𝑛 + 𝑏 + 𝑐 ) 2 for certain values of 𝑎 , 𝑏 , and 𝑐 .