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A1 - any tests you use(a ∞ X n =1 n sin n n 3 1(b ∞ X n...

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MATH 222, Calculus 3, Fall 2011 Assignment 1, due in class Monday, September 19, 2011 1. For each of the following sequences ( a n ), state whether it converges or diverges. For each one that converges, find the limit. (a) a n = cos( π 6 + 1 n 2 ) . (b) a n = 1 n 2 - 2 - n 2 + 2 n . (c) a n = 2 n 50 n 2 . (d) a n = (ln n ) 2 n . (e) a n = sin( 2 ) . 2. For each of the following series, state whether it converges absolutely, con- verges conditionally, or diverges. Justify your answers, including stating
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Unformatted text preview: any tests you use. (a) ∞ X n =1 n sin n n 3 + 1 . (b) ∞ X n =1 (-1) n cos( Ο€ 6 + 1 n 2 ) . (c) ∞ X n =1 (-2) n Β· n ! (3 n )! . (d) ∞ X n =1 (-1) n 1 √ n + 1 + √ n . 1 (e) ∞ X n =1 1 2 n + 3 n ln n . (f) ∞ X n =1 (-1) n ( n n + 1 ) n 2 . 2...
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