In this paper, we investigate the alternating sums of the reciprocal Fibonacci numbers $sumolimits_{k=n}^{mn}{(-1)^k}/{F_{ak+b}}$, where $ain{1,2,3}$ 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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机译：在本文中，我们研究了倒数斐波那契数$ sum nolimits_ {k = n} ^ {mn} {（-1）^ k} / {F_ {ak + b}} $的交替和，其中$ a in {1,2,3 } $和b 展开▼
