For an alternating series whose summands are decreasing in magnitude, the true sum S lies between any two successive partial sums: min {SN, SN+1} ≤ S ≤ max {SN, SN+1}. Consider S = Σ n=1 (−1)n+1 n4 Answer: Nmin = 71 Answer: and write S≈ SN = (a) Find the smallest value of N for which the interval bracketing S in line (*) above has length at most 10-6. N SN + SN+1 2 n=1 (b) Using the N found in part (a), approximate S by the midpoint of the interval implicit in line (*). A spreadsheet may be helpful to calculate the sum SN. (−1)n+1 n4

For an alternating series whose summands are decreasing in magnitude, the true sum S lies between any two successive partial sums: min {SN, SN+1} ≤ S ≤ max {SN, SN+1}. Consider S = Σ n=1 (−1)n+1 n4 Answer: Nmin = 71 Answer: and write S≈ SN = (a) Find the smallest value of N for which the interval bracketing S in line () above has length at most 10-6. N SN + SN+1 2 n=1 (b) Using the N found in part (a), approximate S by the midpoint of the interval implicit in line (). A spreadsheet may be helpful to calculate the sum SN. (−1)n+1 n4

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 81E

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