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Find the "best" |a;b|

Source: German MO 2009 481346

May 15, 2009
calculusinductionalgebra unsolvedalgebra

Problem Statement

Let a sequences: x_0\in [0;1],x_{n\plus{}1}\equal{}\frac56\minus{}\frac43 \Big|x_n\minus{}\frac12\Big|. Find the "best" ∣a;b∣ |a;b| so that for all x0 x_0 we have x2009∈[a;b] x_{2009}\in [a;b]
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