文章基本信息

标题：On the reciprocal sums of the generalized Fibonacci sequences
本地全文：下载
作者：Han Zhang ; Zhengang Wu
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2013
卷号：2013
期号：1
页码：377
DOI：10.1186/1687-1847-2013-377
语种：English
出版社：Hindawi Publishing Corporation
摘要：The Fibonacci sequence has been generalized in many ways. One of them is defined by the relation u n = a u n − 1 + u n − 2 if n is even, u n = b u n − 1 + u n − 2 if n is odd, with initial values u 0 = 0 and u 1 = 1 , where a and b are positive integers. In this paper, we consider the reciprocal sum of u n and then establish some identities relating to ∥ ( ∑ k = n ∞ 1 u k ) − 1 ∥ , where ∥ x ∥ denotes the nearest integer to x. MSC:11B39.
关键词：generalized Fibonacci sequence ; infinite sum ; reciprocal sum