On sums of odd and even terms of the K-Fibonacci numbers

  • Authors

    • Yashwant Panwar Vikram University, Ujjain, INDIA
    • Gajendra P. Rathore Department of Mathematics, College of Horticulture, Mandsaur, India
    • Richa Chawla Vikram University, Ujjain
    2014-07-14
    https://doi.org/10.14419/gjma.v2i3.2587

  • Abstract

    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

    1. A. Chen and H. Chen, "Identities for the Fibonacci Powers", International Journal of Mathemtical Education 39(4) (2008), 534-541.
    2. A. T. Benjamin and J. J. Quinn, “Recounting Fibonacci and Lucas identities”, College Math. J., 30(5): (1999), 359-366.
    3. D. Kalman, R. Mena, The Fibonacci numbers - exposed. Math Mag., 76 (2003), 167–81.
    4. D. Jennings, "On sums the reciprocals of Fibonacci and Lucas Numbers", The Fibonacci Quarterly, 32(1) (1994), 18-21.
    5. H. Belbachir and F. Bencherif, “Sums of products of generalized Fibonacci and Lucas numbers”, arXiv: 0708.2347v1 [math.NT], (2007).
    6. R. S. Melham, "Sums of certain products of Fbonacci and Lucas Numbers", The Fibonacci Quarterly 37(3) (1999), 248-251.
    7. S. Clarly and D. Hemenway, "On sums of cubes of Fibonacci Numbers", In Applications of Fibonacci Numbers 5 (1993), 123-136.
    8. S. Falco´n, on the k-Lucas numbers. International Journal of Contemporary Mathematical Sciences, 6(21) (2011), 1039-1050.
    9. 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.
    10. S. Falco´n, Plaza, A.: On the Fibonacci k-numbers. Chaos, Solitons & Fractals, 32(5) (2007), 1615-1624.
    11. S. Falco´n, Plaza, A.: The k-Fibonacci hyperbolic functions. Chaos, Solitons & Fractals, 38(2) (2008), 409–20.
    12. S. Falco´n, Plaza, A.: The k-Fibonacci sequence and the Pascal 2-triangle. Chaos, Solitons &Fractals, 33(1) (2007), 38-49.
    13. S. Vajda, Fibonacci and Lucas numbers, and the golden section. Theory and applications. Chichester: Ellis Horwood limited (1989).
    14. T. Koshy, “Fibonacci and Lucas Numbers with Applications”, A Wiley-Interscience Publication, New York, (2001).
    15. V. E. Hoggat, Fibonacci and Lucas numbers. Palo Alto, CA: Houghton, (1969).
    16. V. Rajesh and G. Leversha, “Some properties of odd terms of the Fibonacci sequence”, Mathematical Gazette, 88(511): (2004), 85–86.
    17. 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.
    18. Z. Čerin, “Alternating sums of Lucas numbers”, Central European Journal of Mathematics, 3(1): (2005), 1-13.
    19. Z. Čerin, “On sums of squares of odd and even terms of the Lucas sequence”, Proceedings of the 11th Fibonacci Conference, (to appear).
    20. Z. Čerin, “Properties of odd and even terms of the Fibonacci sequence”, Demonstratio Mathematica, 39(1): (2006), 55–60.
    21. 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).
    22. 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

  • How to Cite

    Panwar, Y., Rathore, G. P., & Chawla, R. (2014). On sums of odd and even terms of the K-Fibonacci numbers. Global Journal of Mathematical Analysis, 2(3), 115-119. https://doi.org/10.14419/gjma.v2i3.2587

    Received date: 2014-04-29

    Accepted date: 2014-05-24

    Published date: 2014-07-14