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ERIC Number: EJ891805
Record Type: Journal
Publication Date: 2010
Pages: 6
Abstractor: ERIC
ISBN: N/A
ISSN: ISSN-0819-4564
Sequences of Rational Numbers Converging to Surds
Fletcher, Rodney
Australian Senior Mathematics Journal, v24 n1 p19-24 2010
In this sequence 1/1, 7/5, 41/29, 239/169 and so on, Thomas notes that the sequence converges to square root of 2. By observation, the sequence of numbers in the numerator of the above sequence, have a pattern of generation which is the same as that in the denominator. That is, the next term is found by multiplying the previous term by six and then subtracting the term before the previous one. In order to find the value, that the above sequence of rational numbers converges to, both the difference equation generating the numerators and that generating the denominators has to be solved. This article presents a mathematical solution which finds rational sequences that converge to each of the surds involving prime numbers less than twenty. In this given example, students will learn how to prove that the above sequence converges to square root of 2. (Contains 1 figure.)
Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au
Publication Type: Journal Articles; Reports - Descriptive
Education Level: High Schools; Higher Education
Audience: N/A
Language: English