Question 177
Let $(a_n)_{n \ge 1}$ be a sequence of positive real numbers with the property that
$$
(a_{n+1})^2 + a_n a_{n+2} \le a_n + a_{n+2}
$$
for all positive integers $n$. Show that $a_{2022} \le 1$.
$$
(a_{n+1})^2 + a_n a_{n+2} \le a_n + a_{n+2}
$$
for all positive integers $n$. Show that $a_{2022} \le 1$.