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A Fibonacci 3-subsequence is a subsequence of the type F n , F n+3 , F n+6 , . . . , where F k denotes the kth Fibonacci number. In this article, we investigate the reciprocal sums of the Fibonacci 3-subsequences and obtain several interesting families of identities involving the Fibonacci numbers. MSC: 11B39doi:10.1186/s13662-016-0761-2 fatcat:lnhor5exrjd2jmqkbywltexmqu