math1005ass2 - series 1(5 marks ∞ X n =1(3 x-2 n n 3 n...

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40 marks MATH1005A, Summer2009 Assignment 2 Problem 1 (10 marks) . Show that the sequence defined by a 1 = 2 , a n +1 = 1 3 - a n satisfies 0 < a n 2 and is decreasing. Deduce that the the sequence is convergent and find its limit. Problem 2 . Test for Convergence or divergence. 1 . (5 marks ) X k =1 2 k k ! ( k + 2)! 2 . (5 marks ) X n =1 n 2 - 1 n 3 + 2 n 2 + 5 Problem 3 . Find the radius of convergence and interval of convergence of the power
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Unformatted text preview: series. 1 . (5 marks ) ∞ X n =1 (3 x-2) n n 3 n 2 . (5 marks ) ∞ X n =1 n 2 x n 2 · 4 · 6 · ··· · (2 n ) Problem 4 . Find a power series representation for the function and find the interval of convergence. 1 . (5 marks ) f ( x ) = x 2 a 3-x 3 2 . (5 marks ) f ( x ) = x 2 (1-2 x ) 2 1...
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