In this paper, we investigate the reciprocal sums of even and odd terms in the Fibonacci sequence, and we obtain four interesting families of identities which give the partial finite sums of the even-indexed (resp., odd-indexed) reciprocal Fibonacci numbers and the even-indexed (resp., odd-indexed) squared reciprocal Fibonacci numbers. MSC: 11B39

In this paper, we employ elementary methods to investigate the reciprocal sums of the products of two Fibonacci numbers in several ways. First, we consider the sums of the reciprocals of the products of two Fibonacci numbers and establish five interesting families of identities. Then we extend such analysis to the alternating sums and obtain five analogous results. MSC: 11B39

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: 11B39