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Consider the scries > (-1)k (2k + 1)3* k=1 (a) Show that the scries is convergent. (b) Determine how many terms of the series must be summed to be sure the crror in estimating the sum is less than 10-3. (c) If you cstimate the sum of the series using the first 6 terms, what is the upper bound on the crror in the estimation? 11 3.

Consider the scries > (-1)k (2k + 1)3* k=1 (a) Show that the scries is convergent. (b) Determine how many terms of the series must be summed to be sure the crror in estimating the sum is less than 10-3. (c) If you cstimate the sum of the series using the first 6 terms, what is the upper bound on the crror in the estimation? 11 3.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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Note: In problems on determining scries convergence or divergence, include: • The name of the convergence test or the definition used, • work to show that the test conditions have been met or work to apply the definition, • and a conclusion statement about convergence or divergence.
Transcribed Image Text:Note: In problems on determining scries convergence or divergence, include: • The name of the convergence test or the definition used, • work to show that the test conditions have been met or work to apply the definition, • and a conclusion statement about convergence or divergence.
(-1)* (2k + 1)3 3. Consider the scrics (a) Show that the scries is convergent. (b) Determine how many terms of the scrics must be summed to be sure the crror in cstimating the sum is less than 10 3. (c) If you cstimate the sum of the scries using the first 6 tcrms, what is the upper bound on the crror in the cstimation? 4. Determine whether the scrics is absolutely convergent, conditionally convergent, or divergent. E(-1)*. Vk3 +2 k=1
Transcribed Image Text:(-1)* (2k + 1)3 3. Consider the scrics (a) Show that the scries is convergent. (b) Determine how many terms of the scrics must be summed to be sure the crror in cstimating the sum is less than 10 3. (c) If you cstimate the sum of the scries using the first 6 tcrms, what is the upper bound on the crror in the cstimation? 4. Determine whether the scrics is absolutely convergent, conditionally convergent, or divergent. E(-1)*. Vk3 +2 k=1
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