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Power Serieshard
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If f(x)=∑n=0∞anxnf(x) = \sum_{n=0}^{\infty} a_n x^nf(x)=∑n=0∞​an​xn and g(x)=∑n=0∞bnxng(x) = \sum_{n=0}^{\infty} b_n x^ng(x)=∑n=0∞​bn​xn both represent the same function on an open interval (−δ,δ)(-\delta, \delta)(−δ,δ) around 0, which statement is necessarily true?