On the reciprocal sums of the generalized Fibonacci sequences

被引：11
|
作者：
Zhang, Han [1 ]
Wu, Zhengang [1 ]
机构：
[1] Northwest Univ, Dept Math, Xian, Shaanxi, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2013年
关键词：
generalized Fibonacci sequence; infinite sum; reciprocal sum; INFINITE SUM; PELL;
D O I：
10.1186/1687-1847-2013-377
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Fibonacci sequence has been generalized in many ways. One of them is defined by the relation u(n) = au(n-1) + u(n-2) if n is even, u(n) = bu(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 un and then establish some identities relating to parallel to(Sigma(infinity)(k=n)1/u(k)) (1)parallel to, where parallel to x parallel to denotes the nearest integer to x.
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页数：6
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