Fibonacci and Lucas Numbers as Sums of Binomial Coefficients

Autor/in	Ayoub, Ayoub B.
Titel	Fibonacci and Lucas Numbers as Sums of Binomial Coefficients
Quelle	In: Mathematics and Computer Education, 40 (2006) 3, S.221-225 (5 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0730-8639
Schlagwörter	Mathematical Concepts; History; Mathematics; Problem Solving; Numbers; Computation; College Mathematics; Mathematics Education; Mathematical Formulas + Suchen Sie Ihr Suchwort? Geschichte; Geschichtsdarstellung; Mathematik; Problemlösen; Zahlenraum; Mathematische Bildung; Mathematische Formel
Abstract	The sequence 1, 1, 2, 3, 5, 8, 13, 21, ..., known as Fibonacci sequence, has a long history and special importance in mathematics. This sequence came about as a solution to the famous rabbits' problem posed by Fibonacci in his landmark book, "Liber abaci" (1202). If the "n"th term of Fibonacci sequence is denoted by [f][subscript n], then it may be defined recursively by [f][subscript n+1] = [f][subscript n] + [f][subscript n-1], [f][subscript 0] = 0 and [f][subscript 1] = 1. Many people were fascinated by this sequence, among them the French mathematician Eduoard Lucas (1842-1891). He discovered significant results involving Fibonacci numbers. He also created his own sequence, which is considered a companion to Fibonacci sequence. Lucas sequence: 1, 3, 4, 7, 11, 18, 29, ... is defined recursively by [l][subscript n+1] = [l][subscript n] + [l][subscript n-1], [l][subscript 0] = 2, [l][subscript 1] = 1, where [l][subscript n] represents the "n"th Lucas number. This article will show how to express each of [f][subscript n+1] and [l][subscript n+1] as sums of binomial coefficients. (Contains 1 figure.) (ERIC).
Anmerkungen	MATYC Journal Inc. Mathematics and Computer Education, P.O. Box 158, Old Bethpage, NY 11804. Tel: 516-822-5475; Web site: http://www.macejournal.org
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10