Question 59
Given the sequence of real numbers $x_0 = 1$, $x_1 = 1$,
$$
x_n = \sqrt{\frac{n}{2} + x_{n-1}x_{n-2}}, \quad \text{for } n \ge 2,
$$
determine whether there exists a real number $A$ such that $An \lt x_n \lt An+1$ for all $n \in \mathbb{N}$?
$$
x_n = \sqrt{\frac{n}{2} + x_{n-1}x_{n-2}}, \quad \text{for } n \ge 2,
$$
determine whether there exists a real number $A$ such that $An \lt x_n \lt An+1$ for all $n \in \mathbb{N}$?