Reciprocal Sums of Quintuple Product of Generalized Binary Sequences with Indices

Gaowen Xi1
1College of Mathematics and Physics Chongqing University of Science and Technology Chongaing, 401331, P. R. China

Abstract

By applying the method of generating functions, the purpose of this paper is to give several summations of reciprocals related to the quintuple product of the general second-order recurrence \(\{W_{rn}\}\) for arbitrary positive integers \(r\). As applications, some identities involving Fibonacci and Lucas numbers are obtained.

Keywords: Second order recurrence; Fibonacci number; Lucas num- ber; Quintuple product; Reciprocal 2000 Mathematics Subject Classification: 11B37, 11B39