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Math Algebra and Calculus Add in library

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1. Find the interval of convergence of each power series. (a) ∞ ∑ n=0 2 n (x−3) n n+3 (b) ∞ ∑ n=20 x n logn 2. For what x is the formula 1 1−x = 1+x+x 2 +x 3 +x 4 +··· valid? By first replacing x with −x, then replacing x with x 2 , find a power series for 1 1+x 2 . Hence, or otherwise, find a power series for Z arctanxdx. Use this power series to estimate Z 1 0 arctanxdx to within an accuracy of 0.001. ...

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Tags: Australia  Victoria  Mathematics  Maths Advanced Mathematic Macquarie University MATH136 S214 - Mathematics 

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