Question 176
Let $(a_n)_{n \ge 1}$ be a sequence of non-negative real numbers satisfying
$$
a_{n+1}^2 + a_n a_{n+2} \le a_n + a_{n+2},
$$
for all $n \ge 1$. Prove that the sequence $(a_n)_{n \ge 1}$ is bounded.
$$
a_{n+1}^2 + a_n a_{n+2} \le a_n + a_{n+2},
$$
for all $n \ge 1$. Prove that the sequence $(a_n)_{n \ge 1}$ is bounded.