Question 99
Let $a_{1}, a_{2}, \ldots$ be positive real numbers such that
$$
a_{n+1}^{2}+a_{n} a_{n+2} \leqslant a_{n}+a_{n+2}
$$
for every integer $n \geqslant 1$. Prove that $a_{2023} \leqslant 1$.
$$
a_{n+1}^{2}+a_{n} a_{n+2} \leqslant a_{n}+a_{n+2}
$$
for every integer $n \geqslant 1$. Prove that $a_{2023} \leqslant 1$.