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Suppose that x_1, x_2, x_3, \ldots are positive real numbers for which x^n_n = \sum^{n-1}_{j=0} x^j_n for n = 1, 2, 3, \ldots Prove that \forall n, 2 - \frac{1}{2^{n-1}} \leq x_n < 2 - \frac{1}{2^n}.

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