International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 1, Pages 55-63
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 Odoardo Brugia and Piero Filipponi. 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.
Here we are concerned with series involving generalized Fibonacci
numbers and generalized Lucas numbers . The aim of this paper is to find triples for which the series and (for running from 0 to infinity) are unconcerned at the introduction of the
factor . The results established in this paper generalize the
known fact that the series ( the th Fibonacci number) and the series give the same result, namely .