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# Assign8 - Math 128 ASSIGNMENT 8 Winter 2009 Submit all...

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Math 128 ASSIGNMENT 8 Winter 2009 Submit all problems by 8:20 am on Wednesday, March 25 th in the drop boxes across from MC4066, or in class depending on your instructor’s preference. All solutions must be clearly stated and fully justified . Comment: This assignment is longer than usual. It is strongly recommended that you start working on it early. 1. Find the sum of the given geometric series. a) n =0 3 ( - 1 4 ) n b) n =0 π n 2 3 n - 1 c) n =0 3 + 2 n 3 n +2 2. Apply the n th Term Test (i.e. Divergence Test) or the Comparison Test to decide whether each series converges, converges absolutely, or diverges. a) n =2 n + 1 n - 1 b) n =1 sin nx 2 n , x R c) n =1 2 n n 3 n d) n =0 1 1 + 3 n e) n =1 1 2 - 1 n 2 f) n =0 cos( n 2 ) π n + 3 3. Determine whether each of the following series converges absolutely or diverges by comparison to an appropriate p -series. (You may use the result of example 2 on page 699 of your text.) (i) n =2 1 n - 1 (ii) n =1 ( - 1) n n n 4 + 2 (iii) n =1 arctan 2 n n 2 4. Apply the integral test to determine whether or not each series converges.

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