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Alternating Sums of the Reciprocal

Fibonacci Numbers Andrew Yezhou Wang
School of Mathematical Sciences
University of Electronic Science and Technology of China
Chengdu 611731
P. R. China
mailto:yzwang@uestc.edu.cnyzwang@uestc.edu.cn

Tingrui Yuan
School of Communication and Information Engineering
University of Electronic Science and Technology of China
Chengdu 611731
P. R. China
mailto:ytr2009@icloud.comytr2009@icloud.com

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Abstract:

In this paper, we investigate the alternating sums of the reciprocal Fibonacci numbers $\sum\nolimits_{k=n}^{mn}{(-1)^k}/{F_{ak+b}}$, where $a\in\{1,2,3\}$ and b<a. The integer parts of the reciprocals of these sums are expressed explicitly in terms of the Fibonacci numbers.