6

Part of 2009 German National Olympiad

Problems(1)

Find the "best" |a;b|

Source: German MO 2009 481346

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|

so that for all

x_0

x_{2009}\in [a;b]

calculusinductionalgebra unsolvedalgebra