广义Fibonacci数列两项乘积倒数的有限和  

The Finite Sum of the Reciprocal of Two Products of Generalized Fibonacci Numbers

作　　者：高志贤 杨标桂 GAO Zhixian;YANG Biaogui(College of Mathematics and Informatics,Fujian Normal University,Fuzhou,Fujian 350117,China)

机构地区：[1]福建师范大学数学与信息学院,福建福州350117

出　　处：《宜宾学院学报》2020年第12期48-54,共7页Journal of Yibin University

基　　金：国家自然科学基金资助项目(11761049);福建省自然科学基金资助项目(2017J01398)。

摘　　要：根据广义Fibonacci数列的定义和性质,并利用初等数论的相关理论以及取整函数的性质,证明了两个关于广义Fibonacci数列两项乘积倒数的有限和的恒等式.这两个恒等式揭示了广义Fibonacci数列的某些有限倒数和以及倒数的取整部分与数列本身某些项的联系.再根据研究所得结论,将其应用到Fibonacci数列上.According to the definition and properties of the generalized Fibonacci number,two identities about the finite sum of the reciprocal product of the two terms of the generalized Fibonacci number were proved by using the related knowledge of elementary number theory and the properties of the rounding function.These two identities reveal some finite reciprocal sums of the generalized Fibonacci sequence and the relation between the integral part of the reciprocal and some terms of the sequence itself.According to the conclusion of the study,it is applied to Fibonacci numbers.

关 键 词：广义FIBONACCI数列 有限和 无穷和 倒数 FIBONACCI数列 

分 类 号：O156.4[理学—数学]