On the reciprocal sums of generalized Fibonacci numbers

Abstract

In this paper we obtain some identities for the infinite sum of the reciprocal generalized Fibonacci numbers and the infinite sum of the square of the reciprocal generalized Fibonacci numbers.

On the finite sums of reciprocal Lucas numbers

“…Theorem 1.1 was extended in [2], [3], [7]. On the other hand, Wang and Wen [6] investigated the finite sums of Fibonacci numbers, and considerably extended Theorem 1.1.…”

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 Fibonacci and Lucas numbers

“…Following the work of Ohtsuka and Nakamura [8], diverse results in the same direction have appeared in the literature [1], [3][4][5], [9][10][11][12]. In particular, according to Holliday and Komatsu [5], the infinite sums of reciprocal Lucas numbers satisfy the identities given in Theorem 1.2 below.…”