Unformatted text preview: ( a ) ∞ X n =1 n ! e n , ( b ) ∞ X n =1 √ n n 3n + 1 , ( c ) ∞ X n =2 1 (ln n ) n . QUESTION 3. (4 + 4 + 4 = 12 pts) Determine whether the following series are absolutely convergent, conditionally convergent or divergent. You should state which tests you use, and your reasoning should be clear. ( a ) ∞ X n =1 (1) n arctan( n ) n 2 , ( b ) ∞ X n =2 (1) n ln n , ( c ) ∞ X n =1 (1) n n + 1 10 n + 1 . QUESTION 4. (2 + 10 = 12 pts) (i) What is a power series? (ii) Find the radius of convergence and the interval of convergence of the series ∞ X n =0 2 n ( x3) n n 2 + n + 1 . 1...
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This note was uploaded on 06/04/2011 for the course MAC 3473 taught by Professor Block during the Fall '08 term at University of Florida.
 Fall '08
 BLOCK
 Calculus, Integrals

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