Question

Calendar x Course Home WebWork Math 1417HBG520 X G 11 59 edt to ist - Google Search X + bg.psu.edu/webwork2/Math-141-7HBG-S20/Homework 5/7/?effectiveUser=vqb5190&user=vqb5190&key=OPmT9lyHq7X43XU66923LSKCj6jEDmOF Home Page - Gener. Pearson Course Ho Chapter 19 Dashboard WebWork: Math-1. Home Cheos.com C++ Tutorial @ Electronic library D. DK Homework 5: Problem 7 Previous Problem List Next (1 point) Each of the following statements is an attempt to show that a given series is convergent or divergent not using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.) 1. For all n > 1, - - and the series 2) 1. - and the series – diverges, so by the Comparison Test, the series diverges. es 2 n ln(n) - diverges, so by the Comparison Test, the series - diverges. 2. For all n > 2. 9 Vm-1 In(n) 3. For all n > and the series converges, so by the Comparison Test, the series converges. o oool 4. For and the series converges, so by the Comparison Test, the series - converges. sin” (n) < 6 73 sin' (n) 5. For > 1. and the series and the converges, so by the Comparison Test, the series - converges. 6. For all n > 2. and the series 2) converges, so by the Comparison Test, the series converges. 3 - 4 Note: To get full credit, all answers must be correct. Having all but one correct is worth 50%. Two or more incorrect answers gives a score of 0%. Preview My Answers Submit Answers You have attempted this problem 2 times, Your overall recorded score is 0%. You have unlimited attempts remaining. Email instructor

Answer 1

Problem 7. in is divergent. But the minn) argument is not valid. for example but is convergent. Proof of divergence of antron: 2 a encon) - incon condensation Since &r in divergent, by Inmers in divergent. test & 2. Since th unti and by comparison test z Unt Answer: al in divergent, so is also divergent. En is convergent but the argument is not valid. For example, I . But his divergent. proof lot Convergence : since [ 312 is convergent, by comparison test I en en) is convergend, Answer: IS

A. since a h Comparison test Answer, c it sm) a n then s(m)o tornsill and { this convergent, by is convergent. 5. since sinn comparison test Answer; c) and is convergent, by e simam) in convergent. [Note that sint (m) 21] i na n then fm) >o for nyan g The series { 2 is convergent. r It anaz and bona then lim so an ang and since Ibn is convergent so sam Hence by comparison test { my is convergent. Answer: el

probleme 1. sn't mlo Now 148 n tanto Let an and bra 448n - an +8 Now an _ 748 n + 125 +8 zno+n's - 748 + i naturen 748 as nyo. a finite Poritive number Therefore by limit comparison zest Ibn is convergente since Eanah is convergent) Answer: 8c) -2n +4 Now 120 an 12 n4 _8n²4 bananatnia_an" Also comparison a timiae niomber I t ird convergent. Therefore by limit test , 5 bm=5 2nd to on in is convergent Answer: ACI 3. Let anah and bna 8n + 20 Now an rution - 3412 - 3 bren 8n3+ ano a - 7 as nyo, a tinite porsitive - number Since I am= {n is divergent, by limit comparison zest [ma{ en tom in divergent. Saloon 3 Answer: CD