Question 63
Let $n$ be a positive integer and let $a_1, \dots, a_n$ be $n$ positive integers. Show that
$$
\sum_{k=1}^{n} \frac{\sqrt{a_k}}{1 + a_1 + \dots + a_k} \lt \sum_{k=1}^{n^2} \frac{1}{k}.
$$
$$
\sum_{k=1}^{n} \frac{\sqrt{a_k}}{1 + a_1 + \dots + a_k} \lt \sum_{k=1}^{n^2} \frac{1}{k}.
$$