If a n is a divergent series with positive terms then

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A First Course in Differential Equations with Modeling Applications
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Chapter 6 / Exercise 3
A First Course in Differential Equations with Modeling Applications
Zill
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1. Ifanis a divergent series with positive terms, then(a)limn→∞an6= 0.(b)(-1)nandiverges, too.(c) Ifbn< anfor allnthenbnconverges.(d) None of the above.
anconverges, which conditionon L would guarantee thatbnconverges?
3. If(-1)nanis an alternating series and limn→∞an= 0, which further condition wouldguarantee that the series converges by AST?
4.TRUE or FALSE: Ifanandbnare both convergent series with positive terms,[1]thenanbnis also convergent.5.TRUE or FALSE: IfXn=1anconverges thenXn=1(1 + cos(an))nconverges.[1]
We have textbook solutions for you!
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A First Course in Differential Equations with Modeling Applications
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Chapter 6 / Exercise 3
A First Course in Differential Equations with Modeling Applications
Zill
Expert Verified
(SA) Short answer questions, marks only awarded for a correct final answer, you do not need toshow any work.(a)How many terms would you need to use to estimate the sum ofXn=1(-1)nnwith an[2]error of at most12019?(b)If you used the first 333 terms to estimate the sum ofXn=1(-1)n2nnen, would it be an[2]overestimate or an underestimate?(LA) The remaining questions are long answer questions, please show all of your work.1.Determine all values ofpRfor whichXn=21n(ln(n))pconverges. You can use without[3]proof thatf(x) =1x(ln(x))pis continuous, positive, and decreasing eventually for allpR.
2. Determine whether the following series are convergent or divergent.(a)Xn=1n2+ 3n+ 1n5-n4+n[3](b)Xn=2(-1)nln(n)[3](c)Xn=1lnn(n+ 2)(2n+ 3)2[3]
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