Practice Exam 3 - sl7433 Practice Exam 3 Radin(58415 This...

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sl7433 – Practice Exam 3 – Radin – (58415) 1 This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Determine whether the sequence { a n } con- verges or diverges when a n = ( - 1) n parenleftbigg n + 4 7 n + 4 parenrightbigg , and if it does, find its limit. 1. sequence diverges 2. limit = 1 7 3. limit = 1 4. limit = 0 5. limit = ± 1 7 002 10.0 points Determine whether the series 4 + 3 + 9 4 + 27 16 + · · · is convergent or divergent, and if convergent, find its sum. 1. convergent with sum = 1 16 2. convergent with sum = 9 3. convergent with sum = 16 4. convergent with sum = 1 9 5. divergent 003 10.0 points Determine whether the infinite series summationdisplay n =1 3( n + 1) 2 n ( n + 2) converges or diverges, and if converges, find its sum. 1. converges with sum = 3 2 2. diverges 3. converges with sum = 3 4 4. converges with sum = 3 5. converges with sum = 3 8 004 10.0 points To apply the root test to an infinite series n a n the value of ρ = lim n → ∞ | a n | 1 /n has to be determined. Compute the value of ρ for the series summationdisplay n =1 parenleftbigg 3 n + 4 5 n parenrightbigg 2 n . 1. ρ = 16 25 2. ρ = 9 25 3. ρ = 3 5 4. ρ = 16 9 5. ρ = 4 5 005 10.0 points
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sl7433 – Practice Exam 3 – Radin – (58415) 2 Determine whether the series summationdisplay n =1 ( - 1) n - 1 cos parenleftBig 1 5 n parenrightBig is absolutely convergent, conditionally con- vergent or divergent.
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