In this study, some infinite sums related to the generalized k-Fibonacci numbers have been obtained by using infinite sums related to classic Fibonacci numbers and generalized Fibonacci numbers in literature.
Generalized k-Fibonacci numbers k-Fibonacci numbers sums of integer number sequencesReferans1 Koshy, T. (2001), Fibonacci and Lucas Numbers with Applications, Wiley, New York.Referans2 Falcon S., Plaza A. (2007), On the Fibonacci k-numbers, Chaos, Solitons & Fractals, 32(5), 1615-1624.Referans3 Yosma Z. (2008), Fibonacci and Lucas Numbers, Master's thesis, Graduate School of Natural Sciences, Sakarya University, Sakarya.Referans4 Saba N., Boussayoud, A. (2021), On the bivariate Mersenne Lucas polynomials and their properties, Chaos Solitons & Fractals, vol 146, doi: 10.1016 / j.chaos 2021.110899.2021.Referans5 Chelgham, M., Boussayoud, A. (2021), On the k-Mersenne Lucas numbers, Notes on number theory and discrete mathematics, 27(1), 7-13.Referans6 Saba N., Boussayoud, A., Abderrezzak, A. (2021), Symmetric and generating functions of generalized (p,q) numbers, Kuwait Journal of Science, 48(4).Referans7 Boughaba, S., Boussayoud, A., Saba, N., Kanuri, K. V. V. (2021), A new family of generating functions of binary products of bivariate complex Fibonacci polynomials and Gaussian numbers, Tblisi Mathematical Journal, 14(2), 221-237.Referans8 Taskara N., Uslu K., Gulec H. H. (2010), On the properties of Lucas numbers with binomial coefficients, Applied Mathematics Letters, 23(1), 68-72.Referans9 Gulec H. H., Taskara N., Uslu K. (2013), A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients, Applied Mathematics and Computation, 220, 482-486.Referans10 Uslu K., Taskara N., Uygun S. (2011), The relations among k-Fibonacci, k-Lucas and generalized k-Fibonacci numbers and the spectral norms of the matrices of involving these numbers, Ars Combinatoria, 102, 183-192.Referans11 Uslu K., Taskara N., Kose H. (2011), The generalized k-Fibonacci and k-Lucas Numbers, Ars Combinatoria, 99, 25-32.Referans12 Uslu K., Taskara N., Gulec H. H. (2011), Combinatorial sums of generalized Fibonacci and Lucas numbers, Ars Combinatoria, 99, 139-147.Referans13 Uslu K., Teke M. (2022), Infinite sums related to the generalized Fibonacci numbers, Advances and Applications in Discrete Mathematics, 29(1), 85-96.