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Unformatted text preview: saliyev (is4663) – Quest Assignment 3 – 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 Determine whether the sequence { a n } con verges or diverges when a n = ( − 1) n parenleftbigg 8 n 2 n + 1 parenrightbigg , and if it does, find its limit. 1. limit = ± 4 2. limit = 4 3. limit = 8 4. limit = ± 8 5. limit = 0 6. sequence diverges correct Explanation: After division, 8 n 2 n + 1 = 8 2 + 1 n . Now 1 n → 0 as n → ∞ , so lim n →∞ 8 n 2 n + 1 = 4 negationslash = 0 . Thus as n → ∞ , the values of a n oscillate be tween values ever closer to ± 4. Consequently, the sequence diverges . 002 10.0 points Determine whether the sequence { a n } con verges or diverges when a n = 3 · 7 · 11 ··· (4 n − 1) (4 n ) n , and if it converges, find its limit. 1. converges with limit = 1 4 2. converges with limit = 5 3. converges with limit = 4 4. converges with limit = 0 correct 5. sequence diverges 6. converges with limit = 1 5 Explanation: Since 3 · 7 · 11 ··· · (4 n − 1) (4 n ) n = 3 4 n · 7 4 n · 11 4 n ··· 4 n − 1 4 n ≤ 3 4 n for all n ≥ 1, we see that the inequalities ≤ a n ≤ 3 4 n hold for all n ≥ 1. But lim n →∞ 3 4 n = 0 ....
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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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