Asymptotic behavior of reciprocal sum of two products of Fibonacci numbers

Ho Hyeong Lee, Jong Do Park

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Let {fk}k=1∞ be a Fibonacci sequence with f1= f2= 1. In this paper, we find a simple form gn such that limn→∞{(∑k=n∞ak)−1−gn}=0, where ak=1fk2, 1fkfk+m, or 1f3k2. For example, we show that limn→∞{(∑k=n∞1f3k2)−1−(f3n2−f3n−32+49(−1)n)}=0.

Original languageEnglish
Article number91
JournalJournal of Inequalities and Applications
Volume2020
Issue number1
DOIs
Publication statusPublished - 2020

Keywords

  • Catalan’s identity
  • Convergent series
  • Fibonacci number
  • Reciprocal sum

Fingerprint

Dive into the research topics of 'Asymptotic behavior of reciprocal sum of two products of Fibonacci numbers'. Together they form a unique fingerprint.

Cite this