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1. Consider the series (-1)"+1 n! (a) Determine if the series is absolutely convergent, conditionally convergent, or diverges. be snly. provide a careful argument to prove the type of convergence and name any series tests you apply. (b) What is the smallest integer N so that the partial sum Sy approximates the sum of the series with an error less than 10-2? What is the value of this approximation?

1. Consider the series (-1)"+1 n! (a) Determine if the series is absolutely convergent, conditionally convergent, or diverges. be snly. provide a careful argument to prove the type of convergence and name any series tests you apply. (b) What is the smallest integer N so that the partial sum Sy approximates the sum of the series with an error less than 10-2? What is the value of this approximation?

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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(-1)"+1 1. Consider the series n! (a) Determine if the series is absolutely convergent, conditionally convergent, or diverges. Be sure provide a careful argument to prove the type of convergence and pame any series tests you apply. (b) What is the smallest integer N so that the partial sum SN approximates the sum of the series with an error less than 10-2? What is the value of this approximation?
Transcribed Image Text:(-1)"+1 1. Consider the series n! (a) Determine if the series is absolutely convergent, conditionally convergent, or diverges. Be sure provide a careful argument to prove the type of convergence and pame any series tests you apply. (b) What is the smallest integer N so that the partial sum SN approximates the sum of the series with an error less than 10-2? What is the value of this approximation?
(c) Is the approximation given in part (b) an overestimate or an underestimate? Explain. (Hint: Recall the plot of the partial sum of an alternating serics.)
Transcribed Image Text:(c) Is the approximation given in part (b) an overestimate or an underestimate? Explain. (Hint: Recall the plot of the partial sum of an alternating serics.)
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