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Practice Question 8: Consider the series Σα-Σ 2" 3" +1 n=1 (a) Show that the series a, converges by comparing it with an appropriate geometric series n=1 b, using the comparison test. State explicitly the series b used for comparison. n=1 n=1 (b) If we use the sum of the first k terms a to approximate the sum of Σa, then the error n-1 n-1 R₁ = Σa will be smaller than b. Evaluate Σb, as an expression in k. This serves as a n=k+1 n=k+1 n=k+1 reasonable upper bound for R. (c) Using the upper bound for R, obtained in (b), determine the number of terms required to approximate the series a a accurate to within 0.0003. n=1

Practice Question 8: Consider the series Σα-Σ 2" 3" +1 n=1 (a) Show that the series a, converges by comparing it with an appropriate geometric series n=1 b, using the comparison test. State explicitly the series b used for comparison. n=1 n=1 (b) If we use the sum of the first k terms a to approximate the sum of Σa, then the error n-1 n-1 R₁ = Σa will be smaller than b. Evaluate Σb, as an expression in k. This serves as a n=k+1 n=k+1 n=k+1 reasonable upper bound for R. (c) Using the upper bound for R, obtained in (b), determine the number of terms required to approximate the series a a accurate to within 0.0003. n=1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
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Practice Question 8: Consider the series 2" Σα '3" +1 n=1 (a) Show that the series Σa, converges by comparing it with an appropriate geometric series n=1 busing the comparison test. State explicitly the series b used for comparison. n=1 n=1 (b) If we use the sum of the first k terms a to approximate the sum of Σª, n-1 n-1 R₁ = a, will be smaller than b. Evaluate b, as an expression in k. This serves as a - Σ n=k+1 n=k+1 n=k+1 reasonable upper bound for R₁. (c) Using the upper bound for R, obtained in (b), determine the number of terms required to approximate the series Σa, accurate to within 0.0003. n=1 = n
Transcribed Image Text:Practice Question 8: Consider the series 2" Σα '3" +1 n=1 (a) Show that the series Σa, converges by comparing it with an appropriate geometric series n=1 busing the comparison test. State explicitly the series b used for comparison. n=1 n=1 (b) If we use the sum of the first k terms a to approximate the sum of Σª, n-1 n-1 R₁ = a, will be smaller than b. Evaluate b, as an expression in k. This serves as a - Σ n=k+1 n=k+1 n=k+1 reasonable upper bound for R₁. (c) Using the upper bound for R, obtained in (b), determine the number of terms required to approximate the series Σa, accurate to within 0.0003. n=1 = n
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