Given the series s (-1)"(In(n))² n2 (a) Using the Alternating Series Error bound, determine the smallest value of N for which Is - Sy| < .01. (NOTE: if solve does not work, try nsolve. If that does not work, print the first several terms of the sequence (a,| and observe your value of N). (b) Use the nsum command to find sN for your value of N in part a) and the actual sum s. (In(n))² (c) We now wat to test for absolute convergence, namely, does con- verge. Apply the Integral Test on an appropriate function to show this series does converge. (d) Using the Integral Test Error bound, determine the smallest value of N for which |s - sN| < .01. (Refer to the first part of the hint for part (a) here as well).
Given the series s (-1)"(In(n))² n2 (a) Using the Alternating Series Error bound, determine the smallest value of N for which Is - Sy| < .01. (NOTE: if solve does not work, try nsolve. If that does not work, print the first several terms of the sequence (a,| and observe your value of N). (b) Use the nsum command to find sN for your value of N in part a) and the actual sum s. (In(n))² (c) We now wat to test for absolute convergence, namely, does con- verge. Apply the Integral Test on an appropriate function to show this series does converge. (d) Using the Integral Test Error bound, determine the smallest value of N for which |s - sN| < .01. (Refer to the first part of the hint for part (a) here as well).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Given the series s
(-1)"(In(n))²
n2
(a) Using the Alternating Series Error bound, determine the smallest value of N for
which |s- sy < .01.
(NOTE: if solve does not work, try nsolve. If that does not work, print the first
several terms of the sequence |a,| and observe your value of N).
(b) Use the nsum command to find Sy for your value of N in part a) and the actual
sum s.
(In(n))"
n?
(c) We now want to test for absolute convergence, namely, does
con-
verge. Apply the Integral Test on an appropriate function to show this series does
converge.
(d) Using the Integral Test Error bound, determine the smallest value of N for which
|8 – SN| < .01. (Refer to the first part of the hint for part (a) here as well).
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