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is series to estimat e series be enough

is series to estimat e series be enough

Calculus: Early Transcendentals
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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V12(-1)" 3" (2n + 1) V12(-1)" 3" (2n + 1) Consider the series Note: this was changed from n=0 n=1 Use any test for convergence/divergence to show that the series converges. V12(-1)" (b) It is possible to show that the sum of the series is T, in other words, the series 3" (2n + 1) n=0 converges to the number T. (You do NOT need to prove this, but it can be done somewhat easily using a Taylor series expansion of arctan x.) Suppose you want to use a partial sum of this series to estimate the value of T to an accuracy of within 0.0001. Would using the first 8 terms of the series be enough to ensure you get an accuracy of within 0.0001? (8 terms means the terms where n = 0, 1,2, 3, ....., 7.) Note: This was changed from "7 terms". Hint: Use Theorem 5.14.
Transcribed Image Text:V12(-1)" 3" (2n + 1) V12(-1)" 3" (2n + 1) Consider the series Note: this was changed from n=0 n=1 Use any test for convergence/divergence to show that the series converges. V12(-1)" (b) It is possible to show that the sum of the series is T, in other words, the series 3" (2n + 1) n=0 converges to the number T. (You do NOT need to prove this, but it can be done somewhat easily using a Taylor series expansion of arctan x.) Suppose you want to use a partial sum of this series to estimate the value of T to an accuracy of within 0.0001. Would using the first 8 terms of the series be enough to ensure you get an accuracy of within 0.0001? (8 terms means the terms where n = 0, 1,2, 3, ....., 7.) Note: This was changed from "7 terms". Hint: Use Theorem 5.14.
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