Define a digit to be an element of the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Show that any real number x & [0, 1] can be represented as x = 0.a₂a₂a.....for some sequence of digits {a} n=1

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 32E
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Define a digit to be an element of the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Show that any real number x & [0, 1] can be represented as x = 0.a₂a₂a.....for some sequence
of digits {a}
n=1
Transcribed Image Text:Define a digit to be an element of the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Show that any real number x & [0, 1] can be represented as x = 0.a₂a₂a.....for some sequence of digits {a} n=1
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