Fibonacci 数列倒数的无穷和

王婷婷

数学学报 ›› 2012, Vol. 55 ›› Issue (3) : 517-524.

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PDF(371 KB)
数学学报 ›› 2012, Vol. 55 ›› Issue (3) : 517-524. DOI: 10.12386/A2012sxxb0048
论文

Fibonacci 数列倒数的无穷和

    王婷婷
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On the Infinite Sum of Reciprocal Fibonacci Numbers

    Ting Ting WANG
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文章历史 +

摘要

利用初等方法以及取整函数的性质研究了Fibonacci数列三次倒数的求和问题, 获得了该和式倒数取整后的确切值,也就是给出了一个包含Fibonacci 数列有趣的恒等式.

Abstract

We use the elementary method and the properties of the floor function to study the infinite sums derived from the reciprocals of the cubic of the Fibonacci numbers, and give a new and interesting identity involving the reciprocals of this sums.

关键词

Fibonacci 数列 / 取整函数 / 恒等式

Key words

Fibonacci numbers / floor function / identity

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导出引用
王婷婷. Fibonacci 数列倒数的无穷和. 数学学报, 2012, 55(3): 517-524 https://doi.org/10.12386/A2012sxxb0048
Ting Ting WANG. On the Infinite Sum of Reciprocal Fibonacci Numbers. Acta Mathematica Sinica, Chinese Series, 2012, 55(3): 517-524 https://doi.org/10.12386/A2012sxxb0048

参考文献

[1] Duncan R. L., Applications of uniform distribution to the fibonacci numbers, The Fibonacci Quarterly, 1967,5(2): 137-140.
[2] Wiemann M., Cooper C., Divisibility of an F-L Type Convolution, Applications of Fibonacci Numbers, Vol.9, Kluwer Acad. Publ., Dordrecht, 2004: 267-287.
[3] Prodinger H., On a sum of Melham and its variants, The Fibonacci Quarterly, 2008/2009, 46/47: 207-215.
[4] Ma R., Zhang W. P., Several identities involving the Fibonacci numbers and Lucas numbers, The FibonacciQuarterly, 2007, 45: 164-170.
[5] Ohtsuka H., Nakamura S., On the sum of reciprocal Fibonacci numbers, The Fibonacci Quarterly, 2008/2009,46/47: 153-159.

基金

国家自然科学基金资助项目(11071194)
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