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

被引：1

作者：

Alahmadi, Adel ^{[1
]}

Luca, Florian ^{[1
,2
,3
]}

机构：

[1] King Abdulaziz Univ, Res Grp Algebra Struct & Applicat, POB 1540, Jeddah, Saudi Arabia

[2] Univ Witwatersrand, Sch Maths, 1 Jan Smuts, ZA-2000 Johannesburg, South Africa

[3] Max Plack Inst Math, Bonn, Germany

来源：

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA | 2022年 / 30卷 / 01期

关键词：

Linearly recurrent sequences; Primary; 11B39;

D O I：

10.2478/auom-2022-0002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we that if {F-n((k))}(n >= 0) denotes the k-generalized Fibonacci sequence then for n >= 2 the closest integer to the reciprocal of Sigma(m) (>=) (n) 1/F-m((k)) is F-n((k)) - F-n-1((k)).

引用

页码：31 / 42

页数：12

共 50 条

[31] Diophantine Triples and k-Generalized Fibonacci Sequences
Fuchs, Clemens
Hutle, Christoph
Luca, Florian
Szalay, Laszlo
[J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2018, 41 (03) : 1449 - 1465
[32] ACCELERATION OF THE SUM OF FIBONACCI RECIPROCALS
GRIFFIN, P
[J]. FIBONACCI QUARTERLY, 1992, 30 (02): : 179 - 181
[33] A Binomial Sum of Generalized Fibonacci Numbers
Plaza, Angel
Smith, Jason L.
Abel, Ulrich
Bataille, Michel
Boyadzhiev, Khristo N.
Bradie, Brian
Fedak, I. V.
Fleischman, Dmitry
Frontczak, Robert
Ohtsuka, Hideyuki
Schumacher, Raphael
Stadler, Albert
Terr, David
[J]. FIBONACCI QUARTERLY, 2020, 58 (03): : 275 - 276
[34] On a conjecture about repdigits in k-generalized Fibonacci sequences
Bravo, Jhon J.
Luca, Florian
[J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2013, 82 (3-4): : 623 - 639
[35] ON THE INTERSECTION OF TWO DISTINCT k-GENERALIZED FIBONACCI SEQUENCES
Marques, Diego
[J]. MATHEMATICA BOHEMICA, 2012, 137 (04): : 403 - 413
[36] Sums of reciprocals of Fibonacci numbers
Herrmann, E
[J]. FIBONACCI QUARTERLY, 2004, 42 (04): : 379 - 380
[37] On the zero-multiplicity of the k-generalized Fibonacci sequence
Garcia, Jonathan
Gomez, Carlos A.
Luca, Florian
[J]. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2020, 26 (11-12) : 1564 - 1578
[38] The sum of the squares of two generalized Fibonacci numbers
Howard, FT
[J]. FIBONACCI QUARTERLY, 2003, 41 (01): : 80 - 84
[39] SUM FORMULAE OF GENERALIZED FIBONACCI AND LUCAS NUMBERS
Cerin, Zvonko
Bitim, Bahar Demirturk
Keskin, Refik
[J]. HONAM MATHEMATICAL JOURNAL, 2018, 40 (01): : 199 - 210
[40] ON CERTAIN SERIES OF RECIPROCALS OF FIBONACCI NUMBERS
POPOV, BS
[J]. FIBONACCI QUARTERLY, 1984, 22 (03): : 261 - 265

← 1 2 3 4 5 →