Let be an irrational number. If for rational number (b≥1) 1 < a then 2b² prove that b is equal to one of the convergents of simple continued fraction expansion of Ę.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 24E
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(i) Let be an irrational number. If for rational number
(b21), then prove that
, then prove that
a
b
is equal to
one of the convergents of simple continued fraction
expansion of §.
Transcribed Image Text:(i) Let be an irrational number. If for rational number (b21), then prove that , then prove that a b is equal to one of the convergents of simple continued fraction expansion of §.
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