Some Infinite Sums Related to the \(k\)-Fibonacci Numbers
DOI:
https://doi.org/10.26713/cma.v9i4.838Abstract
In this study, some infinite sums related to the \(k\)-Fibonacci numbers have been obtained by using in…nite sums related to classic Fibonacci numbers in literature.
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F. Büyükkılıç and D. Demirhan, Cumulative growth with Fibonacci approach, golden section and physics, Chaos, Solitons & Fractals 42(1) (2009), 24 – 32.
A. Brousseau, Linear Recursion and Fibonacci Sequences, The Fibonacci Association, San Jose (1971).
L.M. Dabbour, Geometric proportions: The underlying structure of design process for Islamic geometric patterns, Frontiers of Architectural 1(4) (2012), 380 – 391.
V.S. Dimitrov, T.V. Cosklev and B. Bonevsky, Number theoretic transforms over the golden section quadratic field, IEEE Transactions on Signal Processing 43 (1995), 1790 – 1797.
M.S. El Naschie, The Fibonacci code behind super strings and P-Branes, An answer to M. Kaku's fundamental question, Chaos, Solitons & Fractals 31(3) (2007), 537 - 547.
M.S. El Naschie, The golden mean in quantum geometry, Knot Theory and Related Topics, Chaos, Solitons & Fractals 10(8) (1999), 1303 – 1307.
S. Falcón and A. Plaza, On the Fibonacci k-numbers, Chaos, Solitons & Fractals 32(5) (2007), 1615 – 1624.
M. Hejazi, Geometry in nature and Persian architecture, Building and Environment 40(10) (2005), 1413 – 1427.
T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley, New York (2001).
A.A. Ocal, N. Tuglu and E. Altinisik, On the representation of k-generalized Fibonacci and Lucas numbers, Applied Mathematics and Computation 170(1) (2005), 584 – 596.
A.D. Richard, The Golden Ratio and Fibonacci Numbers, World Scientific Publishing, Singapore (1997).
R.M. Ricketts, The biologic signijkance of the divine proportion and Fibonacci series, American Journal of Orthodontics 81(5) (1982), 351 – 370.
N.N. Vorob'ev, Fibonacci Numbers, Blaisdell Publishing Company, New York (1961).
R. Ward, On robustness properties of beta encoders and golden ratio encoders, IEEE Transactions on Information Theory (2008), 4324 – 4334.
Z. Yosma, Fibonacci and Lucas Numbers, Master's thesis, Graduate School of Natural Sciences, Sakarya University, Sakarya (2008).
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