The reciprocal sums of even and odd terms in the Fibonacci sequence

[摘要] 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.

[学科分类] 数学（综合）

[关键词] Fibonacci sequence;even and odd term;reciprocal sum;11B39