Question 102
Let $(a_n)_{n \ge 0}$ and $(b_n)_{n \ge 0}$ be sequences of real numbers such that $a_0 \gt 1/2$, $a_{n+1} \ge a_n$, and $b_{n+1} = a_n(b_n + b_{n+2})$, for all non-negative integers $n$. Show that the sequence $(b_n)_{n \ge 0}$ is bounded.