On sums of odd and even terms of the K-Fibonacci numbers
DOI:
https://doi.org/10.14419/gjma.v2i3.2587Abstract
In this paper, we define some properties of sums of k-Fibonacci numbers. Also we present the sum of consecutive members of k-Fibonacci numbers and the same thing for even and for odd k-Fibonacci numbers. Mainly, Binet’s formula will be used to establish properties of k-Fibonacci numbers.
Keywords: K-Fibonacci Numbers, K-Lucas Numbers, Binet’s Formula.
References
A. Chen and H. Chen, "Identities for the Fibonacci Powers", International Journal of Mathemtical Education 39(4) (2008), 534-541.
A. T. Benjamin and J. J. Quinn, “Recounting Fibonacci and Lucas identities”, College Math. J., 30(5): (1999), 359-366.
D. Kalman, R. Mena, The Fibonacci numbers - exposed. Math Mag., 76 (2003), 167–81.
D. Jennings, "On sums the reciprocals of Fibonacci and Lucas Numbers", The Fibonacci Quarterly, 32(1) (1994), 18-21.
H. Belbachir and F. Bencherif, “Sums of products of generalized Fibonacci and Lucas numbers”, arXiv: 0708.2347v1 [math.NT], (2007).
R. S. Melham, "Sums of certain products of Fbonacci and Lucas Numbers", The Fibonacci Quarterly 37(3) (1999), 248-251.
S. Clarly and D. Hemenway, "On sums of cubes of Fibonacci Numbers", In Applications of Fibonacci Numbers 5 (1993), 123-136.
S. Falco´n, on the k-Lucas numbers. International Journal of Contemporary Mathematical Sciences, 6(21) (2011), 1039-1050.
S. Falco´n, On the Lucas Triangle and its Relationship with the k-Lucas numbers. Journal of Mathematical and Computational Science, 2(3) (2012), 425-434.
S. Falco´n, Plaza, A.: On the Fibonacci k-numbers. Chaos, Solitons & Fractals, 32(5) (2007), 1615-1624.
S. Falco´n, Plaza, A.: The k-Fibonacci hyperbolic functions. Chaos, Solitons & Fractals, 38(2) (2008), 409–20.
S. Falco´n, Plaza, A.: The k-Fibonacci sequence and the Pascal 2-triangle. Chaos, Solitons &Fractals, 33(1) (2007), 38-49.
S. Vajda, Fibonacci and Lucas numbers, and the golden section. Theory and applications. Chichester: Ellis Horwood limited (1989).
T. Koshy, “Fibonacci and Lucas Numbers with Applications”, A Wiley-Interscience Publication, New York, (2001).
V. E. Hoggat, Fibonacci and Lucas numbers. Palo Alto, CA: Houghton, (1969).
V. Rajesh and G. Leversha, “Some properties of odd terms of the Fibonacci sequence”, Mathematical Gazette, 88(511): (2004), 85–86.
Y. Yazlik, N. Yilmaz and N. Taskara, “On the Sums of Powers of k-Fibonacci and k-Lucas Sequences” Selçuk J. Appl. Math., Special Issue (2012), 47-50.
Z. Čerin, “Alternating sums of Lucas numbers”, Central European Journal of Mathematics, 3(1): (2005), 1-13.
Z. Čerin, “On sums of squares of odd and even terms of the Lucas sequence”, Proceedings of the 11th Fibonacci Conference, (to appear).
Z. Čerin, “Properties of odd and even terms of the Fibonacci sequence”, Demonstratio Mathematica, 39(1): (2006), 55–60.
Z. Čerin and G. M. Gianella, “On sums of Pell numbers”, Acc. Sc. Torino – Atti Sc. Fis. 140, xx-xx. web.math.pmf.unizg.hr/~cerin/c165.pdf, (2006).
Z. Čerin and G. M. Gianella, “On sums of squares of Pell-Lucas numbers”, INTEGERS: Electronic Journal of Combinatorial Number Theory, 6, #A15, (2006).
Downloads
Additional Files
Published
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal''s published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
