Let \(x_1 = 2\) and

\(x_{n+1} = x_n^2 - x_n +1\)

for \(n \geq 1\)

Prove that

\(1 - \frac {1}{2^{2^{n-1}}} < \frac {1}{x_1} + \frac {1}{x_2} + ... + \frac {1}{x_n} < 1 - \frac {1}{2^{2^n}}\).

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