Prove: If the power series k=0 akxk and k=0 bkxk havethe same sum on an interval (r, r)
Chapter 9, Problem 46(choose chapter or problem)
Prove: If the power series \(\sum_{k=0}^{\infty} a_{k} x^{k} \text { and } \sum_{k=0}^{\infty} b_{k} x^{k}\) have the same sum on an interval \((-r, r) \text {, then } a_{k}=b_{k}\) for all values of \(k\).
Equation Transcription:
Text Transcription:
Sum of k=0 infinity a_k x^k
Sum of k=0 infinity b_k x^k
(-r,r)
a_k=b_k
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