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V12(–1)" 37 (2n + 1) 1. Consider the series n=1 Use any test for convergence/divergence to show that the series converges. 12(-1)" 3" (2n + 1) (b) It is possible to show that the sum of the series is T, in other words, the series n=1 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 7 terms of the series be enough to ensure you get an accuracy of within 0.0001?

V12(–1)" 37 (2n + 1) 1. Consider the series n=1 Use any test for convergence/divergence to show that the series converges. 12(-1)" 3" (2n + 1) (b) It is possible to show that the sum of the series is T, in other words, the series n=1 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 7 terms of the series be enough to ensure you get an accuracy of within 0.0001?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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V12(-1)" 37 (2n + 1) 1. Consider the series n=1 (a) Use any test for convergence/divergence to show that the series converges. V12(-1)" 3" (2n + 1) (You do NOT need to prove this, but it can be done somewhat easily using a (b) It is possible to show that the sum of the series is T, in other words, the series n=1 converges to the number a. Taylor series expansion of arctan x.) Suppose you want to use a partial sum of this series to estimate the value of 7 to an accuracy of within 0.0001. Would using the first 7 terms of the series be enough to ensure you get an accuracy of within 0.0001? Hint: Use Theorem 5.14.
Transcribed Image Text:V12(-1)" 37 (2n + 1) 1. Consider the series n=1 (a) Use any test for convergence/divergence to show that the series converges. V12(-1)" 3" (2n + 1) (You do NOT need to prove this, but it can be done somewhat easily using a (b) It is possible to show that the sum of the series is T, in other words, the series n=1 converges to the number a. Taylor series expansion of arctan x.) Suppose you want to use a partial sum of this series to estimate the value of 7 to an accuracy of within 0.0001. Would using the first 7 terms of the series be enough to ensure you get an accuracy of within 0.0001? Hint: Use Theorem 5.14.
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