On the sum of reciprocal generalized Fibonacci numbers

2015/03/03 by Pingzhi Yuan, Yuan, Pingzhi, Zilong He +3 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #11B37 #11B39 #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #FOS: Mathematics #Fractal and DNA sequence analysis #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1503.00803

openalex publication_date 2015/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibonacci numbers.

Cited by

• The asymptotic estimation for two classes of generalized Fibonacci sub-sequences
• The inverse of the (alternating) infinite sum of the reciprocal of the weighted sum for generalized Fibonacci sub-sequences

Related

• Four New Generalized Fibonacci Number Summation Identities
• Some Weighted Generalized Fibonacci Number Summation Identities, Part 2
• Some Weighted Generalized Fibonacci Number Summation Identities, Part 1
• Sums of products of generalized Fibonacci and Lucas numbers
• The inverse of the (alternating) infinite sum of the reciprocal of the weighted sum for generalized Fibonacci sub-sequences