Question 38
Let $n$ be a positive integer and let $a_1, a_2, \ldots, a_n$ be real numbers with $a_1 + a_2 + \ldots + a_k \le k$ for all $k \in \{1, 2, \ldots, n\}$. Show that
$$
\frac{a_1}{1} + \frac{a_2}{2} + \ldots + \frac{a_n}{n} \le \frac{1}{1} + \frac{1}{2} + \ldots + \frac{1}{n}.
$$
$$
\frac{a_1}{1} + \frac{a_2}{2} + \ldots + \frac{a_n}{n} \le \frac{1}{1} + \frac{1}{2} + \ldots + \frac{1}{n}.
$$