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### Exam4_1_F04

Course: MTHSC 108, Fall 2008
School: Clemson
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Word Count: 347

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Sc Mth 108: Exam 4 Sections 12.2-10 Fall 2004 Version 1 1 General Directions: Show all work analytically. When determining the convergence or divergence of a series, state the test (one on the handout) you use and analytically show in detail how you use it. If asked to approximate the sum and/or discuss a bound on the error for an alternating series, assume the alternating series satisfies the conditions of...

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Sc Mth 108: Exam 4 Sections 12.2-10 Fall 2004 Version 1 1 General Directions: Show all work analytically. When determining the convergence or divergence of a series, state the test (one on the handout) you use and analytically show in detail how you use it. If asked to approximate the sum and/or discuss a bound on the error for an alternating series, assume the alternating series satisfies the conditions of the Alternating Series Test. Summarize your conclusion in verbal sentence form. ------------------------------------------------------------------------------------------------------------------------For problems 1-4, determine if the series converges or diverges. If a series is geometric and convergent, find its sum. (9 points each) 1. n =1 (3n 2 + n )2 2n 3 / 2 + n 2. n =1 cos n 2 Mth Sc 108: Exam 4 Sections 12.2-10 Fall 2004 Version 1 2 3. 5 3 + 9 27 81 + + 5 25 125 4. n =1 e n n2 (Use the integral test.) Mth Sc 108: Exam 4 Sections 12.2-10 Fall 2004 Version 1 3 For problems 5 and 6, determine whether the series is absolutely convergent, conditionally convergent, or diverges. (9 points each) 5. n =1 ( 1) n 4n 2 / 3 3 Mth Sc 108: Exam 12.2-10 Fall 4 Sections 2004 Version 1 4 6. n =1 ( 1) n +1 2n + 1 n! 7. For the series n =1 ( 1) n +1 2n + 1 find the smallest value of n such that the partial sum n! sn approximates the actual sum with an error less than 0.01. (6 points) Mth Sc 108: Exam 4 Sections 12.2-10 Fall 2004 Version 1 5 8.For the power series n =1 ( x + 1) n 3n 2 n a. What is the center? (2 points) b. Analytically find the radius of convergence. (10 points) c. Determine the interval of convergence. Be sure to include a check for convergence at the endpoints of the interval. (6 points) Mth Sc 108: Exam 4 Sections 12.2-10 Fall 2004 Version 1 6 9. For the function f ( x ) = sin x a. Find the Maclaurin series...

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