On the Reciprocal Sums of Products of Balancing and Lucas-Balancing Numbers

Abstract

Recently Panda et al. obtained some identities for the reciprocal sums of balancing and Lucas-balancing numbers. In this paper, we derive general identities related to reciprocal sums of products of two balancing numbers, products of two Lucas-balancing numbers and products of balancing and Lucas-balancing numbers. The method of this paper can also be applied to even-indexed and odd-indexed Fibonacci, Lucas, Pell and Pell–Lucas numbers.

Keywords

• balancing numbers
• Lucas-balancing numbers
• Fibonacci numbers
• reciprocal
• floor function