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Test4 - ∞ ± n =1 1 √ n 1 3 3 Use Comparison test to...

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MAC 2312-01,02,03 Calculus II Test 4 November 21, 2008 Dr. Jungmin Choi Name Instructions. 1. This test has 6 pages including this page. There are 7 problems. 2. Show all your work. You may not receive any credit from a correct answer, if there is no relevant work leading to the answer. 3. Do not separate the pages of the test. If any pages do become separated, write your name on them and point them out to your instructor when you turn in your test. 4. You are not allowed to use a calculator. 5. Please turn off all cell phones and pagers and remove all headphones. Problem Points Score 1 10 2 10 3 10 4 10 5 15 6 15 7 30 Total 100 1
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1. Determine whether the sequence converges or diverges. If it converges, find the limit. (5 points each) (a) 1 1 2 + 1 , 2 2 2 + 1 , 3 3 2 + 1 , 4 4 2 + 1 , ... (b) a n = sin 1 n 2
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2. Use Integral test to determine whether the series is convergent or divergent. (10 points)
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Unformatted text preview: ∞ ± n =1 1 √ n + 1 3 3. Use Comparison test to determine whether the series is convergent or divergent. (10 points) ∞ ± n =1 1 + cos n 10 n 4. Use Alternating series test to determine whether the series is convergent or divergent. (10 points) ∞ ± n =1 (-1) n n n 2 + 1 4 5. Use Ratio test to determine whether the series is convergent or divergent. (15 points) ∞ ± n =1 n ! 2 n 6. Use Root test to determine whether the series is convergent or divergent. (15 points) ∞ ± n =1 3 n n n 5 7. Test the series for convergence or divergence. (a) ∑ ∞ k =1 1 5 k (10 points) (b) ∑ ∞ n =1 cos n (10 points) (c) ∑ ∞ n =1 n + 1 4 n (10 points) 6...
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