review3 - Valencia(drv252 Review 3 Zheng(58355 This...

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Valencia (drv252) – Review 3 – Zheng – (58355) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the n th term, a n , of an infinite series n =1 a n when the n th partial sum, S n , of the series is given by S n = 4 n n + 1 . 1. a n = 5 n ( n + 1) 2. a n = 5 2 n 3. a n = 2 n 4. a n = 4 n ( n + 1) 5. a n = 5 2 n 2 6. a n = 2 n 2 002 10.0 points Let f be a continuous, positive, decreasing function on [3 , ). Compare the values of the integral A = integraldisplay 20 3 f ( t ) dt and the series B = 19 summationdisplay n =3 f ( n ) . 1. A = B 2. A > B 3. A < B 003 10.0 points To apply the root test to an infinite series k a k , the value of ρ = lim k → ∞ | a k | 1 /k has to be determined. Compute the value of ρ for the series summationdisplay k =1 3 k k (ln k + 7) k . 1. ρ = 7 2. ρ = 21 3. ρ = 3 4. ρ = 5. ρ = 0 004 10.0 points Determine whether the series summationdisplay n =0 parenleftbigg 4 7 parenrightbigg n/ 2 is convergent or divergent, and if convergent, find its sum. 1. convergent with sum = 7 - 2 7 2. convergent with sum = 7 - 2 2 3. convergent with sum = 7 7 - 2 4. convergent with sum = 2 7 - 2 5. divergent 005 10.0 points
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Valencia (drv252) – Review 3 – Zheng – (58355) 2 Decide which, if any, of the following series converge.
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