Question 161
The sequence of real numbers $(x_n)$ is defined by
$$
x_1 = 0,\ x_2 = 2 \text{ and } x_{n+2} = 2^{-x_n} + \frac{1}{2} \text{ for all } n \ge 1.
$$
Prove that the sequence converges and find its limit.
$$
x_1 = 0,\ x_2 = 2 \text{ and } x_{n+2} = 2^{-x_n} + \frac{1}{2} \text{ for all } n \ge 1.
$$
Prove that the sequence converges and find its limit.