Question 39
Let $a_1, a_2, \dots, a_9$ be a sequence of numbers satisfying $0 \lt p \le a_i \le q$ for each $i = 1, 2, \dots, 9$. Prove that
$$
\frac{a_1}{a_9} + \frac{a_2}{a_8} + \dots + \frac{a_9}{a_1} \le 1 + \frac{4(p^2 + q^2)}{pq}.
$$
$$
\frac{a_1}{a_9} + \frac{a_2}{a_8} + \dots + \frac{a_9}{a_1} \le 1 + \frac{4(p^2 + q^2)}{pq}.
$$