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138assgn7 - MATH 138 Assignment 7 Series(part II Spring...

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MATH 138 Assignment 7 Spring 2009 Series (part II). Submit all problems marked (*) and the Maple Lab 3 by 12:30 p.m. on Friday, July 3. 1. Use the integral test to decide if the series is convergent or not. (a) n =1 1 (2 n +1) 3 (b) ( * ) n =1 ne - n (c) ( * ) n =1 1 n +4 (d) n =1 n +2 n +1 2. Determine whether the series is convergent or divergent. (a) n =1 1 n 2 +4 (b) n =1 ln n n 3 (c) ( * ) n =1 n 2 n 3 +1 (d) ( * ) n =1 1 n (ln n ) 2 (e) n =1 e 1 /n n 2 (f) ( * ) n =1 n 2 e n 3. Find the values of p for which the series is convergent. (a) ( * ) n =1 n (1 + n 2 ) p . (b) n =1 ln n n p . 4. (a) Use the sum of the first 10 terms to estimate the sum of the series n =1 1 /n 2 . How good is the estimate? (b) Improve the estimate using the inequality s n + Z n +1 f ( x ) dx X n =1 a n s n + Z n f ( x ) dx with n = 10. (c) Find
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