a. Explanation Given: The series is ∑ k = 1 ∞ e − k . Result used: “Let f be a continuous, positive, decreasing function, for x ≥ 1 , and let a k = f ( k ) for k = 1 , 2 , 3 , ⋯ . Let S = ∑ k = 1 ∞ a k be a convergent series and let S n = ∑ k = 1 n a k be the sum of the first n times of the series. The remainder satisfies R n = s − s n , R n < ∫ n ∞ f ( x ) d x and the exact value of the series is bounded as S n + ∫ n + 1 ∞ f ( x ) d x b . To determine To find: The number of terms are needed to ensure that the remainder R n is less than 10 − 3 . c . To determine To find: The lower and upper bounds on the exact value of the series. d . To determine To find: The interval at which the value of the series lie, if the value is approximated to ten terms of the series.

Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book

2nd Edition

ISBN: 9780321954237

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 8.4, Problem 40E

To determine

To find: An upper bound for the remainder in terms of n.

To determine

To find: The number of terms are needed to ensure that the remainder Rn is less than 10−3.

To determine

To find: The lower and upper bounds on the exact value of the series.

To determine

To find: The interval at which the value of the series lie, if the value is approximated to ten terms of the series.

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Chapter 8.4, Problem 39E

Chapter 8.4, Problem 41E

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Chapter 8 Solutions

Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book

Ch. 8.1 - Prob. 1QC Ch. 8.1 - Prob. 2QC Ch. 8.1 - Prob. 3QC Ch. 8.1 - Prob. 4QC Ch. 8.1 - Prob. 5QC Ch. 8.1 - Define sequence and give an example.Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E

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An upper bound for the remainder in terms of n .

Solution Summary: The author calculates an upper bound for the remainder in terms of n, using e-n.

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To find: An upper bound for the remainder in terms of n.

To find: The number of terms are needed to ensure that the remainder Rn is less than 10−3.

To find: The lower and upper bounds on the exact value of the series.

To find: The interval at which the value of the series lie, if the value is approximated to ten terms of the series.

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Chapter 8 Solutions