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International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 1, Pages 55-63
http://dx.doi.org/10.1155/S0161171200001873

A curious property of series involving terms of generalized sequences

Fondazione Ugo Bordoni, Via B. Castiglione 59, Roma I-00142, Italy

Received 13 April 1998; Revised 11 September 1998

Copyright © 2000 Hindawi Publishing Corporation. 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

Here we are concerned with series involving generalized Fibonacci numbers Un(p,q) and generalized Lucas numbers Vn(p,q). The aim of this paper is to find triples (p,q,r) for which the series Un(p,q)/rn and Vn(p,q)/rn (for r running from 0 to infinity) are unconcerned at the introduction of the factor n. The results established in this paper generalize the known fact that the series Fn/2n (Fn the nth Fibonacci number) and the series nFn/2n give the same result, namely 2/5.