For an alternating series whose summands are decreasing in magnitude, the true sum S lies between any two successive partial sums: Consider S = ∞ n=1 (*) (−1)n+1 n³ Answer: Nmin = and write Answer: S≈ min {SN, SN+1} ≤ S≤ max {SN, SN+1}. (−1)n+1 n³ SN = (a) Find the smallest value of N for which the interval bracketing S in line (*) above has length at most 10-5. SN + SN+1 2 N n=1 (b) Using the N found in part (a), approximate S by the midpoint of the interval implicit in line (*). A spreadshe may be helpful to calculate the sum SN.

For an alternating series whose summands are decreasing in magnitude, the true sum S lies between any two successive partial sums: Consider S = ∞ n=1 () (−1)n+1 n³ Answer: Nmin = and write Answer: S≈ min {SN, SN+1} ≤ S≤ max {SN, SN+1}. (−1)n+1 n³ SN = (a) Find the smallest value of N for which the interval bracketing S in line () above has length at most 10-5. SN + SN+1 2 N n=1 (b) Using the N found in part (a), approximate S by the midpoint of the interval implicit in line (*). A spreadshe may be helpful to calculate the sum SN.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 81E

See similar textbooks