**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.)

Descriptors: Numbers, Mathematics Instruction, Problem Solving, Equations (Mathematics), Spreadsheets, Secondary School Mathematics, College Mathematics, Validity, Mathematical Logic

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

**Sponsor:**N/A

**Authoring Institution:**N/A