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Unformatted text preview: has a limit as n . (7) (a) What does the Ratio Test say about the series X n =1 n n 2 + 1 ? (b) Does the above series converge or diverge? (8) Give an example of a series such that X n =1 a n converges but X n =1  a n  diverges. Give reasons for convergence and divergence. (9) (a) Find a formula expressing (1x )2 as a power series centered at 0. For which values of x is your formula correct? (b) Evaluate the sum X n =1 n 3 n . (10) Evaluate the indenite integral Z x 1x 4 dx as a power series, and state its radius of convergence. (11) Find the Maclaurin series of xex and its radius of convergence. (12) Find the power series of 1 4x centered at 2 and its radius of convergence....
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This note was uploaded on 01/11/2010 for the course MATH 115 at Yale.
 '08
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 Integrals

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