FORMULA BINET DAN JUMLAH n SUKU PERTAMA PADA GENERALISASI BILANGAN FIBONACCI DENGAN METODE MATRIKS

Purnamayanti Purnamayanti, Thresye Thresye, Na'imah Hijriati

Abstract



Fibonacci numbers are defined as sequences of precise numbers is the sum of the previous two tribes. Binet in 1875 proposes an Fn formula capable of calculating the nth number of numbers it is faster without having to recalculate as much as n times, which then known as Binet formulas or formulas. The purpose of this study is to learn the formation of the Binet formula, forming a generalization of Binet formulas on Fibonacci numbers p-degree, look for the number of n tribes first in Fibonacci numbers p-degree with linear algebraic approach especially the use of matrices.

Keywords


Fibonacci matrix, Binet formula, diagonalization, matrix Vandermonde.

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References


Anton, H. 1994. Aljabar Linier Elementer. Terjemahan Pantun Silaban dan I Nyoman Susila. Erlangga, Jakarta.

Ayres, F. 1984. Matriks. Terjemahan I Nyoman Susila. Erlangga, Jakarta.

Dunlap, R.A. 1997. The Golden Ratio and Fibonacci Numbers. Word

Scientific, United State of America.

Fraleigh, J.B. 1995. Linier Algebra. Addison-Wesley. United State of America

Kilic, E. 2007. European Journal of Combinatorics. The Binet Formula, sums and representations of generalized Fibonacci p-numbers. TOBB ETU

University of Economics and Technologi, Mathematics Departement,

Sogutozu, Ankara, Turkey

Stakhov, A.P. 2006. Chaos, Solitions & Fractals. Fibonacci Matrices, A

Generalization of The “Cassini Formula”, and A New Coding Theory.

Taganrog State University of Radio Engineering, Rusia.




DOI: https://doi.org/10.20527/epsilon.v6i1.80

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