Question: Please solve #7. Subject: Real Analysis, Topic: Power Series. This is the only information provided. 7. Suppose that the sequence (|c. /Call ) converges to

Please solve #7. Subject: Real Analysis, Topic: Power Series. This is the only information provided.

7. Suppose that the sequence (|c. /Call ) converges to a real number r. Prove that r is the radius of convergence of the power series Jo c.(x -a) (be sure to properly handle the special case r = () On the other hand, prove that if the above sequence diverges to co, then the radius of convergence of the power series is OC

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