Question 119
Fix an integer $n \ge 2$ and let $a_1, a_2, \dots, a_n$ be real numbers in the closed interval $[1, 2024]$. Prove that
$$
\sum_{i=1}^{n} \frac{1}{a_i} (a_1 + a_2 + \dots + a_i) \gt \frac{1}{44} n(n + 33).
$$
$$
\sum_{i=1}^{n} \frac{1}{a_i} (a_1 + a_2 + \dots + a_i) \gt \frac{1}{44} n(n + 33).
$$