Geodesic
Alternating sums of the reciprocal Fibonacci numbers
Journal of integer sequences, Tome 20 (2017) no. 1
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.
Classification : 11B39, 11B37
Keywords: Fibonacci number, alternating sum, reciprocal 
@article{JIS_2017__20_1_a7,
     author = {Wang,  Andrew Yezhou and Yuan,  Tingrui},
     title = {Alternating sums of the reciprocal {Fibonacci} numbers},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {1},
     zbl = {1367.11026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_1_a7/}
}
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Wang,  Andrew Yezhou; Yuan,  Tingrui. Alternating sums of the reciprocal Fibonacci numbers. Journal of integer sequences, Tome 20 (2017) no. 1. http://geodesic.mathdoc.fr/item/JIS_2017__20_1_a7/