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33

Part of PEN M Problems

Problems(1)

M 33

Source:

5/25/2007
The sequence {xn}n≥1 \{x_{n}\}_{n \ge 1} is defined by x_{1} \equal{} 2, x_{n \plus{} 1} \equal{} \frac {2 \plus{} x_{n}}{1 \minus{} 2x_{n}}\;\; (n \in \mathbb{N}). Prove that a) x_{n}\not \equal{} 0 for all n∈N n \in \mathbb{N}, b) {xn}n≥1 \{x_{n}\}_{n \ge 1} is not periodic.
trigonometryinductionRecursive Sequences