Explanation Given: The series is ∑ k = 1 ∞ 1 k 5 . Result used: If the function f ( k ) = a k , where f is a continuous, positive and decreasing function for x ≥ 1 and S n = ∑ k = 1 n a n is convergent, then 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 < ∑ k = 1 ∞ a k < S n + ∫ n ∞ f ( x ) d x . Explanation: Given: The series is ∑ k = 1 ∞ 1 k 5 . Calculation: Obtain the sum of the series ∑ k = 1 ∞ 1 k 5 by evaluation the first 20 terms of the series

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

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

Publisher: PEARSON

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Chapter 8, Problem 62RE

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To approximate: The series ∑k=1∞1k5 by evaluating the first 20 terms; Compute an upper bound for the error in the approximation.

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Chapter 8, Problem 61RE

Chapter 8, Problem 63RE

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Chapter 8 Solutions

Calculus: Early Transcendentals (2nd Edition)

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 Ch. 8.1 - Given the series k=1k, evaluate the first four...Ch. 8.1 - The terms of a sequence of partial sums are...Ch. 8.1 - Consider the infinite series k=11k. Evaluate the...Ch. 8.1 - Explicit formulas Write the first four terms of...Ch. 8.1 - Explicit formulas Write the first four terms of...

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To approximate: The series ∑ k = 1 ∞ 1 k 5 by evaluating the first 20 terms; Compute an upper bound for the error in the approximation.

Solution Summary: The author calculates the sum of the series by evaluating the first 20 terms and calculating an upper bound for the error in the approximation.

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To approximate: The series ∑k=1∞1k5 by evaluating the first 20 terms; Compute an upper bound for the error in the approximation.

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Chapter 8 Solutions