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Unformatted text preview: ∑ ∞ n =0 c n (1 2 ) n is convergent. (a) Does it follow that ∑ ∞ n =0 c n ( 1 3 ) n is convergent? Answer: Yes (it is within the radius of convergence) (b) Does it follow that ∑ ∞ n =1 c n ( 1 2 ) n is convergent? Answer: No (if the radius of convergence is 1/2, it could diverge) (c) Does it follow that ∑ ∞ n =1  c n (1) n  is divergent? Answer: No (maybe the c n were already positive and the ROC is 5) 3. (2 points) Give an example of a nonpolynomial function that is equal to its MacLaurin series on its entire domain. Possible answers: e x , cos x, sin x 2...
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 Fall '08
 Reshetiken
 Derivative, Power Series, Mathematical Series, Convergence, Radius of convergence

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