The limit of reciprocal sum of some subsequential fibonacci numbers

Ho Hyeong Lee, Jong Do Park

Research output: Contribution to journalArticlepeer-review

Abstract

This paper deals with the sum of reciprocal Fibonacci numbers. Let f0 = 0, f1 = 1 and fn+1 = fn + fn-1for any n ∈ N. In this paper, we prove new estimates on [Formula Presented], where m ∈ N and 0 ≤ ℓ ≤ m- 1. As a consequence of some inequalities, we prove on [Formula Presented] And we also compute the explicit value of [Formula Presented]. The interesting observation is that the value depends on m(n + 1) + ℓ.

Original languageEnglish
Pages (from-to)12379-12394
Number of pages16
JournalAIMS Mathematics
Volume6
Issue number11
DOIs
Publication statusPublished - 2021

Keywords

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

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