The limit of reciprocal sum of some subsequential fibonacci numbers

Ho Hyeong Lee; Jong Do Park

doi:10.3934/math.2021716

The limit of reciprocal sum of some subsequential fibonacci numbers

Research output: Contribution to journal › Article › peer-review

Abstract

This paper deals with the sum of reciprocal Fibonacci numbers. Let f₀ = 0, f₁ = 1 and f_n+1 = f_n + f_n-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 language	English
Pages (from-to)	12379-12394
Number of pages	16
Journal	AIMS Mathematics
Volume	6
Issue number	11
DOIs	https://doi.org/10.3934/math.2021716
Publication status	Published - 2021

Keywords

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

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10.3934/math.2021716

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title = "The limit of reciprocal sum of some subsequential fibonacci numbers",

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.",

keywords = "Catalan{\textquoteright}s identity, Convergent series, Fibonacci number, Floor function, Reciprocal sum",

author = "Lee, {Ho Hyeong} and Park, {Jong Do}",

note = "Funding Information: This work was supported by NRF-2018R1D1A1B07050044 from National Research Foundation of Korea (Second author). The authors would like to appreciate the referees for their helpful comments. Publisher Copyright: {\textcopyright} 2021 the Author(s), licensee AIMS Press.",

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doi = "10.3934/math.2021716",

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AU - Lee, Ho Hyeong

AU - Park, Jong Do

N1 - Funding Information: This work was supported by NRF-2018R1D1A1B07050044 from National Research Foundation of Korea (Second author). The authors would like to appreciate the referees for their helpful comments. Publisher Copyright: © 2021 the Author(s), licensee AIMS Press.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Catalan’s identity

KW - Convergent series

KW - Fibonacci number

KW - Floor function

KW - Reciprocal sum

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ER -

The limit of reciprocal sum of some subsequential fibonacci numbers

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Keywords

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