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Unformatted text preview: saliyev (is4663) – Quest Assignment 4 – rodin – (54520) 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Rewrite the series 6 2 3 2 sin 3 5 6 2 3 3 sin 4 6 + 6 2 3 4 sin 5 7 + . . . using summation notation. 1. sum = ∞ k = 3 2 3 k 1 6 sin k k + 1 2. sum = ∞ k = 1 2 3 k 6 sin( k + 2) k + 4 3. sum = ∞ k = 3 2 3 k 1 6 sin k k + 2 correct 4. sum = 20 k = 2 2 3 k 6 sin( k + 1) k + 3 5. sum = 15 k = 3 2 3 k 1 6 sin k k + 2 Explanation: The given series is an infinite series, so two of the answers must be incorrect because they are finite series written in summation notation. Starting summation at k = 3 we see that the general term of the infinite series is a k = 6 2 3 k 1 sin k k + 2 . Consequently, sum = ∞ k = 3 2 3 k 1 6 sin k k + 2 . 002 10.0 points Determine whether the series is convergent or divergent. If it is convergent, find its sum. ∞ n =1 11 n ( n + 3) 1. 198 11 2. 77 18 3. 121 18 correct 4. divergent 5. 11 198 Explanation: 003 10.0 points If the n th partial sum of an infinite series is S n = 2 n 2 1 n 2 + 3 , what is the sum of the series? 1. sum = 1 3 2. series diverges 3. sum = 2 correct 4. sum = 2 3 5. sum = 1 Explanation: By definition sum = lim n →∞ S n = lim n →∞ 2 n 2 1 n 2 + 3 . Thus sum = 2 . saliyev (is4663) – Quest Assignment 4 – rodin – (54520) 2 004 10.0 points Find the n th term, a n , of an infinite series ∞ n = 1 a...
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This note was uploaded on 09/15/2011 for the course M 55565 taught by Professor Rusin during the Spring '11 term at University of Texas.
 Spring '11
 RUSIN

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