# Q3 - Version 085/ABBBB DGQ03 gilbert(55485 This print-out...

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Unformatted text preview: Version 085/ABBBB DGQ03 gilbert (55485) This print-out should have 3 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points so After division, 5n6 = 7n3 + 4 5n3 , 4 7+ 6 n 1 Which one of the following properties does the series (-1)n 4 n4 + 3 n=1 5 5n6 - > 0 3+4 7n 7 as n . Thus by the Limit Comparison test, the infinite series n-3 have? 1. conditionally convergent 2. divergent 3. absolutely convergent correct Explanation: n=1 5n6 7n3 + 4 p will converge if and only if the infinite series 1 n-3p n=1 converges. But by the Integral test we know that the series n=1 1 np 002 10.0 points Find all values of p for which the infinite series p 5n6 7n3 + 4 n=1 converges if and only if p > 1. Consequently, the given series will converge if and only if -3p > 1, i.e., when p < - 003 1 . 3 converges? 1 1. p > 3 2. p < -3 3. p > 7 3 10.0 points Which, if any, of the following series converge? 1 1 1 1 A. 1 + + + + + . . . 2 3 4 5 B. n=1 1 1 + n2 1 4. p < - correct 3 7 5. p < - 3 6. p > 3 Explanation: 1. 2. 3. 4. both of them A only B only correct neither of them Version 085/ABBBB DGQ03 gilbert (55485) Explanation: 2 A. Series is n=1 1 1 . Use f (x) = 1/2 .Then n x f (x) dx 1 is divergent, so series diverges 1 . Then B. Use f (x) = 1 + x2 f (x) dx 1 is convergent (tan-1 integral), so series converges. ...
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Q3 - Version 085/ABBBB DGQ03 gilbert(55485 This print-out...

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