Question 4
Let the real sequence $(x_n)$ be defined by $x_1=0$, $x_2=2$ and
$$x_{n+2}=2^{-x_n}+\frac12\qquad(n=1,2,3,\ldots).$$
Prove that it converges to a finite limit as $n\to+\infty$, and find the limit.
$$x_{n+2}=2^{-x_n}+\frac12\qquad(n=1,2,3,\ldots).$$
Prove that it converges to a finite limit as $n\to+\infty$, and find the limit.