9.4-LA-solutions-Integral_Test_and_P-Series

9.4-LA-solutions-Integral_Test_and_P-Series - MthSc 108-9.4...

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MthSc 108-9.4 (Integral Test) & P-Series Provide your work and answers on a separate sheet of paper. Do not use a calculator! State the name of the test you use and the specific criteria for that test which allows you to make the determination about convergence or divergence for each problem. Give a concluding statement in a complete (non-mathematical) written sentence. Easy Warm-Up Problems: 1. Find the nth or general term of the series. State if the series converges or diverges. 1 + 1 4 3 + 1 9 3 + 1 16 3 + 1 25 3 + L = 1 n 2 3 = n = 1 1 n 2 3 n = 1 Since p = 2 3 1, by the p-series test the series 1 n 2 3 n = 1 diverges. 2. Write out the first 4 terms of the series and state if the series converges or diverges. 2 n 9 n n = 1 = 2 3 1 n 3 2 = n = 1 2 3 1 1 3 2 + 1 2 3 2 + 1 3 3 2 + 1 4 3 2 + ... Since p = 3 2 > 1, by the p-series test, 1 n 3 2 n = 1 converges, and thus the series 2 n 9 n n = 1 converges. Harder Problems: 3. Use the integral test if applicable to determine if the series is convergent or divergent. Show all your work. ln
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9.4-LA-solutions-Integral_Test_and_P-Series - MthSc 108-9.4...

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