关于二阶线性递归序列倒数和的对称性  

The Symmetry Property of Reciprocal Sums of 2-order Linear Recursive Sequences

作　　者：胡宏[1] 

机构地区：[1]淮阴师范学院数学系,江苏淮安223001

出　　处：《淮阴师范学院学报（自然科学版）》2002年第1期23-25,共3页Journal of Huaiyin Teachers College;Natural Science Edition

基　　金：江苏省教育厅自然科学基金资助项目(0 1KJD110 0 0 5)

摘　　要：设A和是B不等于 0的实数,｛wn｝n∈z 是二阶递归序列且满足递归关系:wn+ 2 =Awn+ 1-Bwn(n∈z).本文研究了二阶线性递归序列｛wn｝n∈z 的倒数和的对称性,并且得出了关于｛wn｝n∈z 的二个收敛的无穷级数,推广I.J.Good文中的主要结论.Let A and B be two nonzero real numbers, and z denote the set of integers, and let {w n} satisfy the recursive relation w n+2 =Aw n+1 -Bw n(n∈z) . In this paper we study the symmetry property of reciprocals sums of 2 order linear recursive sequences, and determine two infinite series involving 2 order linear recursive sequences is convergent. The results provide vast generalizations of corresponding results in .

关 键 词：二阶线性递归序列 LUCAS序列 对称性 

分 类 号：O156.1[理学—数学]