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APMO 2000 Problem 1

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Compute the sum S=∑i=0101xi31−3xi+3xi2S=\sum_{i=0}^{101} \frac{x_{i}^{3}}{1-3 x_{i}+3 x_{i}^{2}} for xi=i101x_{i}=\frac{i}{101}.

Dataset text NuminaMath olympiads. Quoted with source.

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