On the Reciprocal Sums of Product of Fibonacci and Lucas Numbers

Abstract

In this paper, we study the reciprocal sums of product of Fibonacci and Lucas numbers. Interesting identities are obtained related to the numbers $\sum_{k=n}^{\infty}1/F_{k}L_{k+m}$ and $\sum_{k=n}^{\infty}1/L_{k}F_{k+m}$, $m \geq 0$.