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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 non-polynomial 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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