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Quest Assignment 4-solutions

# Quest Assignment 4-solutions - saliyev(is4663 Quest...

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saliyev (is4663) – Quest Assignment 4 – rodin – (54520) 1 This print-out should have 10 questions. Multiple-choice 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 .

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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 n when the n th partial sum of the series is S n = 2 n n + 1 .
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