Journal of Integer Sequences, Vol. 20 (2017), Article 17.1.4

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

Tingrui Yuan
School of Communication and Information Engineering
University of Electronic Science and Technology of China
Chengdu 611731
P. R. China

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.

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(Concerned with sequence A000108.)

Received July 9 2016; revised version received December 24 2016. Published in Journal of Integer Sequences, December 26 2016.

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