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The meaning of the decimal representation of a number 0.d₁d₂d3... (where the digit d, is one of the numbers 0, 1, 2, ..., 9) is as follow 0.d₁d₂d3d4 d4 d₁ + d₂ d3 10 10² 103 + 104 Show that this series converges for all choices of d₁, d₂... n=1 do n 10" For i = 1, 2, . n, let d; be a single digit integer. For i = 1, 2, , n, dn 10" ? ✓ 00 Thus, 0.d₁d₂d3 n=1 Since the summation ... 9 10" 00 n=1 00 = n=1 10" + is a ---Select--- with dnis convergent by ---Select--- 10" --Select--- ? ✓ 10' This inequality of terms gives the following. it is convergent.

The meaning of the decimal representation of a number 0.d₁d₂d3... (where the digit d, is one of the numbers 0, 1, 2, ..., 9) is as follow 0.d₁d₂d3d4 d4 d₁ + d₂ d3 10 10² 103 + 104 Show that this series converges for all choices of d₁, d₂... n=1 do n 10" For i = 1, 2, . n, let d; be a single digit integer. For i = 1, 2, , n, dn 10" ? ✓ 00 Thus, 0.d₁d₂d3 n=1 Since the summation ... 9 10" 00 n=1 00 = n=1 10" + is a ---Select--- with dnis convergent by ---Select--- 10" --Select--- ? ✓ 10' This inequality of terms gives the following. it is convergent.

Algebra & Trigonometry with Analytic Geometry
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 73E
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The meaning of the decimal representation of a number 0.d₁d₂d3... (where the digit d; is one of the numbers 0, 1, 2, 0.dddd4 d₂ d3 10² 103 Show that this series converges for all choices of d₁, d₂... dn n=1107 ? ✓ 00 9 ΣΤΟ 10" n = 1 Since the summation Thus, 0.d₁d₂d3. = 00 n For i = 1, 2,. ... n, let d; be a single digit integer. For i = 1, 2,, N, - 10" n=1 = 9 10 n = 1 d1 10 + + + is a ---Select--- d4 104 +... with ---Select--- 'n is convergent by ---Select--- 10" 9 10 9) is as follows. This inequality of terms gives the following. it is convergent. "
Transcribed Image Text:The meaning of the decimal representation of a number 0.d₁d₂d3... (where the digit d; is one of the numbers 0, 1, 2, 0.dddd4 d₂ d3 10² 103 Show that this series converges for all choices of d₁, d₂... dn n=1107 ? ✓ 00 9 ΣΤΟ 10" n = 1 Since the summation Thus, 0.d₁d₂d3. = 00 n For i = 1, 2,. ... n, let d; be a single digit integer. For i = 1, 2,, N, - 10" n=1 = 9 10 n = 1 d1 10 + + + is a ---Select--- d4 104 +... with ---Select--- 'n is convergent by ---Select--- 10" 9 10 9) is as follows. This inequality of terms gives the following. it is convergent. "
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