Geodesic
Alternating sums of the reciprocal Fibonacci numbers
Journal of integer sequences, Tome 20 (2017) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Wang, Andrew Yezhou and Yuan, Tingrui},
     title = {Alternating sums of the reciprocal {Fibonacci} numbers},
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     language = {en},
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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/