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Power Serieshard
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If two power series ∑n=0∞an(x−1)n\sum_{n=0}^{\infty} a_n (x-1)^n∑n=0∞​an​(x−1)n and ∑n=0∞bn(x−1)n\sum_{n=0}^{\infty} b_n (x-1)^n∑n=0∞​bn​(x−1)n represent the same function on the open interval (0,2)(0, 2)(0,2), which must be true?