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Fibonacci and k Lucas Sequences as Series of Fractions

In this paper, we defined new relationship between k Fibonacci and k Lucas sequences using continued fractions and series of fractions, this approach is different and never tried in k Fibonacci sequence literature.

Author(s):

  • A. D. Godase, V. P. College, Vaijapur, Maharashtra, India
  • M. B. Dhakne, Dr. B.A.M. University, Aurangabad, Maharashtra, India

Keywords:

k -Fibonacci sequence, k -Lucas sequence, Recurrence relation

URL:

https://mjis.chitkara.edu.in/index.php/mjis/article/view/81/41

References:

A.D.Godase, M.B.Dhakne, On the properties of k Fibonacci and k Lucas numbers, International Journal of Advances in Applied Mathematics and Mechanics, 02 (2014), 100-106.

A. D. Godase, M. B. Dhakne, Fundamental Properties of Multiplicative Coupled Fibonacci Sequences of Fourth Order Under Two Specific Schemes, International Journal of Mathematical Archive, 04, No. 6 (2013), 74 – 81.

A. D. Godase, M. B. Dhakne, Recurrent Formulas of The Generalized Fibonacci Sequences of Fifth Order, “International Journal of MathematicalArchive”, 04, No. 6 (2013), 61 – 67.

A. D. Godase, M. B. Dhakne, Summation Identities for k Fibonacci and k Lucas Numbers using Matrix Methods, “International Journal of Mathematics and Scientific Computing” , 05, No. 2 (2015), 75 – 78.

A. D. Godase, M. B. Dhakne, Determinantal Identities for k Lucas Sequence, “Journal of New Theory”, 12 (2015), 01 – 07.

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