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m22sum05q4 - series compares(a ∞ X n =1 1 √ n 2-4(b ∞...

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MATH 22 Quiz 4 Take-home August 3, 2005 NAME: (Last, First) 1. Are the terms b n = n n +1 increasing, decreasing or “not monotone”? Does the series X n =1 ( - 1) n n n + 1 converge? Give a reason. 2. Find the ratio of the terms of the series X n =1 2 n n 3 n +1 . Simplify your answer. (The correct answer includes “n”.) Find the limit of the ratio of the terms, and determine whether the series con- verges.
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2 3. Determine whether the given series converges or diverges. If you use comparison, state clearly why the comparision series converges or diverges; and how the given
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Unformatted text preview: series compares. (a) ∞ X n =1 1 √ n 2-4 (b) ∞ X n =1 4 n-1 5 n (c) ∞ X n =1 n-1 n 3 + 1 4. Find the Taylor polynomial of the indicated degree for the given function about the given point. (a) f ( x ) = √ 1 + x 2 ; x = 0 , degree 2. (b) f ( x ) = e-x ; x = 0 , degree 4. (c) Find the Taylor polynomial P 3 ( x, 0) of the function f ( x ) = √ 1 + x....
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