On the reciprocal sums of products of Fibonacci and Lucas numbers

Abstract

In this paper, we study the reciprocal sums of products of Fibonacci and Lucas numbers. Some identities are obtained related to the numbers ∞ k=n 1/F k L k+m and ∞ k=n 1/L k F k+m , m ≥ 0.

Some results on the infinite sums of reciprocal generalized Fibonacci numbers

“…Following the work of Ohtsuka and Nakamura, diverse results in the same direction have been reported in the literature [1][2][3][4][5], [7][8][9][10], [13], [14]. In particular, Wang and Zhang [14] considered the reciprocal sums of even-indexed and odd-indexed Fibonacci numbers, and obtained Theorem 1.2 below.…”

On the Reciprocal Sums of Products of Two Generalized Bi-Periodic Fibonacci Numbers

“…where • is the floor function. Following the work of Ohtsuka and Nakamura, diverse results for the numbers of the form {G n } = S(G 0 , G 1 , a, a) have been reported in the literature (see [7][8][9][10][11][12][13][14][15] and references cited therein).…”

On the Sum of Reciprocal of Polynomial Applied to Higher Order Recurrences

“…Choi and Choo [12] derived the formulas for the following sums of reciprocals of products of Fibonacci and Lucas numbers:…”