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# A09 - x-3 n 2 n 1(d ∞ X n =1 10 n x n n 10 3 Suppose ∞...

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Math 138 – Fall 2011 Assignment 9 Due Monday Nov 21 (in the drop box by 12 noon) Hand in the following: 1. Determine whether the series is absolutely convergent, conditionally convergent, or divergent. (a) X n =1 ( - 1) n - 1 n 4 (b) X n =1 n ! e n (c) X n =1 ( - 1) n n n 3 + 2 (d) X n =1 ( - 1) n +1 n 2 2 n n ! (e) X n =1 cos(1 /n ) n 2 2. Find the radius of convergence, as well as the interval of convergence for the following power series. (a) X n =1 3 n n ! x n (b) X n =1 1 4 n ( x + 1) n (c) X n =1 ( -

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Unformatted text preview: x-3) n 2 n + 1 (d) ∞ X n =1 10 n x n n 10 3. Suppose ∞ X n =0 a n x n has a radius of convergence R , where 0 < R < ∞ . Let k > ,k ∈ Z , what is the radius of convergence of ∞ X n =0 a n x kn ? 4. Consider the series ∞ X n =1 a n where a n satisﬁes a n +1 = a n-a n +1 n , a 1 = 1; Determine if the series above converges or diverges. 2...
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A09 - x-3 n 2 n 1(d ∞ X n =1 10 n x n n 10 3 Suppose ∞...

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