关于Lucas数的无限倒数和的等式  

Equation of the Sum of Reciprocal Lucas Numbers

作　　者：陈小芳[1] 

机构地区：[1]渭南师范学院数理学院数学系,陕西渭南714099

出　　处：《西华大学学报（自然科学版）》2017年第4期83-86,92,共5页Journal of Xihua University:Natural Science Edition

基　　金：国家自然科学基金(11501419);陕西省教育厅科学研究计划专项项目(15JK1262);渭南师范学院军民融合项目(16JMR11);渭南师范学院科研项目(17YKS11);省重点扶持学科基础数学学科基金资助

摘　　要：根据Lucas数列的定义,利用初等数论的相关知识,讨论了Lucas数列的倒数的无限和以及Lucas数的平方数的倒数无限和,对其和求倒数,利用取整函数,得到有关Lucas数列的2个重要的等式.According to the definition of the Lucas sequence, the relevant knowledge of elementary number theory was utilized to analyze infinite sums derived from the reciprocals of the Lucas numbers and infinite sums derived from the reciprocals of the square of the Lucas numbers. By applying the floor function to the reciprocals of these sums, two important equations related to the sequence of Lucas numbers were obtained.

关 键 词：LUCAS数列 FIBONACCI数列 取整 LUCAS数 倒数和 

分 类 号：O156.2[理学—数学]