1. bookVolume 30 (2022): Edition 1 (February 2022)
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License
Format
Magazine
eISSN
1844-0835
Première parution
17 May 2013
Périodicité
1 fois par an
Langues
Anglais
access type Accès libre

On the sum of the reciprocals of k-generalized Fibonacci numbers

Publié en ligne: 12 Mar 2022
Volume & Edition: Volume 30 (2022) - Edition 1 (February 2022)
Pages: 31 - 42
Reçu: 07 May 2021
Accepté: 25 Jul 2021
Détails du magazine
License
Format
Magazine
eISSN
1844-0835
Première parution
17 May 2013
Périodicité
1 fois par an
Langues
Anglais
Abstract

In this note, we that if { Fn(k) }n0 {\left\{ {F_n^{\left( k \right)}} \right\}_{n \ge 0}} denotes the k-generalized Fibonacci sequence then for n ≥ 2 the closest integer to the reciprocal of mn1/Fm(k) \sum\nolimits_{m \ge n} {1/F_m^{\left( k \right)}} is Fn(k)Fn1(k) F_n^{\left( k \right)} - F_{n - 1}^{\left( k \right)} .

Keywords

MSC 2010

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