Question 54
Let $n \ge 2$ be a positive integer and let $a_1, a_2, \dots, a_n$ be positive numbers such that $a_1 \le a_2$, $a_1 + a_2 \le a_3$, $a_1 + a_2 + a_3 \le a_4$, $\dots$, $a_1 + a_2 + \dots + a_{n-1} \le a_n$. Prove that
$$
\frac{a_1}{a_2} + \frac{a_2}{a_3} + \frac{a_3}{a_4} + \dots + \frac{a_{n-1}}{a_n} \le \frac{n}{2}.
$$
$$
\frac{a_1}{a_2} + \frac{a_2}{a_3} + \frac{a_3}{a_4} + \dots + \frac{a_{n-1}}{a_n} \le \frac{n}{2}.
$$