Article 11 INTEGERS 11A (2011) Proceedings of Integers Conference 2009 ON THE SUM OF RECIPROCAL GENERALIZED FIBONACCI NUMBERS Sarah H. Holliday Dept. of Mathematics, Southern Polytechnic State University, Marietta, Georgia shollida@spsu.edu Takao Komatsu 1 Graduate School of Science and Technology, Hirosaki University, Hirosaki, Japan komatsu@cc.hirosaki-u.ac.jp Received: 8/22/09, Revised: 5/27/10, Accepted: 6/2/10, Published: 3/9/11 Abstract The Fibonacci Zeta functions are defined by ζ F (s)=  ∞ k=1 F -s k . Several aspects of the function have been studied. In this article we generalize the results by Ohtsuka and Nakamura, who treated the partial infinite sum  ∞ k=n F -s k for all positive integers n. 1. Introduction The so-called Fibonacci and Lucas Zeta functions , defined by ζ F (s)= ∞  n=1 1 F s n and ζ L (s)= ∞  n=1 1 L s n , respectively, have been considered in several different ways. In [8] the analytic continuation of these series is discussed. In [2] it is shown that the numbers ζ F (2), ζ F (4), ζ F (6) (respectively, ζ L (2), ζ L (4), ζ L (6)) are algebraically independent, and that each of ζ F (2s) (respectively, ζ L (2s)) (s =4, 5, 6,... ) can be written as a rational (respectively, algebraic) function of these three numbers over Q. Similar results are obtained in [2] for the alternating sums ζ * F (2s) := ∞  n=1 (−1) n+1 F 2s n  respectively, ζ * L (2s) := ∞  n=1 (−1) n+1 L 2s n  (s =1, 2, 3,... ) . 1 Supported in part by the Grant-in-Aid for Scientific Research (C) (No. 18540006), the Japan Society for the Promotion of Science.