Question: Suppose that |ak| |bk| for large k. Prove that if k=0 bkxk converges on an open interval I, then k=0 akxk also converges on I.

Suppose that |ak| |bk| for large k. Prove that if ∑∞k=0 bkxk converges on an open interval I, then ∑∞k=0 akxk also converges on I. Is this result true if open is omitted?

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