Midterm 2 Practice Solutions - MATH 6BWinter 2016 Vector...

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Essential Calculus: Early Transcendentals
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Chapter 8 / Exercise 5
Essential Calculus: Early Transcendentals
Stewart
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MATH 6B–Winter 2016Vector Calculus IIStudy Guide Midterm 2: Extra Problems1. Recognize a geometric series. In the following examples, give a check mark to the geometric series andtwo check marks to the convergent geometric series. Find their sum when possible. If the series is notgeometric, can you determine their convergence/divergence?
2. Identify what is the optimal test to determine convergence of a series. For the following series, write atleast one test that will determine their convergence/divergence, describe how you will use each test, andstate the reason why the test applies.(a)Xn=1n!2nRatio Test
→∞2n+1n!2n= limn→∞(b)Xn=11n3+ 1Limit Comparison Test
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Essential Calculus: Early Transcendentals
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Chapter 8 / Exercise 5
Essential Calculus: Early Transcendentals
Stewart
Expert Verified
(c)Limit ComparisonTestCompare it withbn= 1/n3, thenlimn1→∞rn3

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