Advances and Applications in Discrete Mathematics

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INFINITE SUMS RELATED TO THE GENERALIZED FIBONACCI NUMBERS

Authors

  • Kemal Uslu
  • Mustafa Teke

Keywords:

analysis, serial sum, convergence.

DOI:

https://doi.org/10.17654/0974165822007

Abstract

Fibonacci numbers and applications related to these numbers are frequently encountered both in daily life and in various fields of science and engineering. There are many studies to sum expressions on these numbers [1]. However, in later periods, generalized Fibonacci numbers, which are the more general version of Fibonacci and Lucas numbers, and also new number sequences such as $k$-Fibonacci numbers by Sergio Falcon have entered into the literature [2]. In this study, some sums of generalized Fibonacci numbers have been investigated and compared with previously obtained sums of Fibonacci and Lucas numbers, which are the special cases of these sums.

Received: September 22, 2021
Accepted: November 21, 2021

References

T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley, New York, 2001.

S. Falcon and A. Plaza, On the Fibonacci k-numbers, Chaos Solitons Fractals 32(5) (2007), 1615-1624.

Z. Yosma, Fibonacci and Lucas numbers, Master’s Thesis, Graduate School of Natural Sciences, Sakarya University, Sakarya, 2008.

N. Saba and A. Boussayoud, On the bivariate Mersenne Lucas polynomials and their properties, Chaos Solitons Fractals 146 (2021), Paper No. 110899, 6 pp. doi: 10.1016/j.chaos2021.110899.2021.

M. Chelgham and A. Boussayoud, On the k-Mersenne Lucas numbers, Notes on Number Theory and Discrete Mathematics 27(1) (2021), 7-13.

N. Saba, A. Boussayoud and A. Abderrezzak, Symmetric and generating functions of generalized numbers, Kuwait Journal of Science 48(4) (2021). https://doi.org/10.48129/kjs.v48i4.10074.

S. Boughaba, A. Boussayoud, N. Saba and K. V. V. Kanuri, A new family of generating functions of binary products of bivariate complex Fibonacci polynomials and Gaussian numbers, Tbilisi Mathematical Journal 14(2) (2021), 221-237.

N. Taskara, K. Uslu and H. H. Gulec, On the properties of Lucas numbers with binomial coefficients, Appl. Math. Lett. 23(1) (2010), 68-72.

H. H. Gulec, N. Taskara and K. Uslu, A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients, Appl. Math. Comput. 220 (2013), 482-486.

K. Uslu, N. Taskara and S. Uygun, The relations among k-Fibonacci, k-Lucas and generalized k-Fibonacci numbers and the spectral norms of the matrices of involving these numbers, Ars Combin. 102 (2011), 183-192.

K. Uslu, N. Taskara and H. Kose, The generalized k-Fibonacci and k-Lucas numbers, Ars Combin. 99 (2011), 25-32.

K. Uslu, N. Taskara and H. H. Gulec, Combinatorial sums of generalized Fibonacci and Lucas numbers, Ars Combin. 99 (2011), 139-147.

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Published

2021-12-20

Issue

Vol. 29 No. 1 (2022)

Section

Articles

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How to Cite

INFINITE SUMS RELATED TO THE GENERALIZED FIBONACCI NUMBERS. (2021). Advances and Applications in Discrete Mathematics, 29(1), 85-96. https://doi.org/10.17654/0974165822007

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