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Cody · Q6

Sequences & series

A sequence is defined by

xn+1=1−2xnxn3,0<xn<(12)2/3.x_{n+1}=\frac{1-2x_n\sqrt{x_n}}3,\qquad0<x_n<\left(\frac12\right)^{2/3}.

If xn→ax_n\to a, find aa.

A13\frac13
B25\frac25
C67\frac67
D12\frac12
E14\frac14

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