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13

Part of PEN M Problems

Problems(1)

M 13

Source:

5/25/2007
The sequence {xn}\{x_{n}\} is defined by x0∈[0,1],  xn+1=1−∣1−2xn∣.x_{0}\in [0, 1], \; x_{n+1}=1-\vert 1-2 x_{n}\vert. Prove that the sequence is periodic if and only if x0x_{0} is irrational.
functioninductionpigeonhole principlecalculusintegrationRecursive Sequences