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section11-4

section11-4 - ∞ X n =1 1 n 2 converges by the Limit...

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Supplemental Exercises for Section 11.4 Which of the following series converge and which diverge? Verify your answer. 1. n =1 1 n n + 7 2. n =2 1 n 3 n - 1 3. n =1 6 n + 1 n 3 + 4 4. n =1 n - 1 n 3 n 2 + 2 5. n =1 1 n n 2 + 5 6. n =1 ln n n ( n + 10) 7. n =1 n 3 2 n ( n + 5) Selected Answers 1. Because lim n →∞ 1 n n +7 1 n = 1 and because n =1 1 n diverges, by the Limit Comparison Test, n =2 1 n n - 1 diverges. 3. Because lim n →∞ 6 n +1 n 3 +4 1 n 2
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Unformatted text preview: ∞ X n =1 1 n 2 converges, by the Limit Comparison Test ∞ X n =1 6 n + 1 n 3 + 4 converges. 6. By using L’Hˆ opital’s rule lim n →∞ ln n n ( n +10) 1 n 3 2 = 0. Thus because ∞ X n =1 1 n 3 2 converges, by the Limit Comparison Test ∞ X n =1 ln n n ( n + 10) converges. 1...
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