Question 76
Determine all positive integers $n$ such that the inequality
$$
\sqrt{x-1} + \sqrt{x-2} + \cdots + \sqrt{x-n} \lt x
$$
holds for every real number $x \ge n$.
$$
\sqrt{x-1} + \sqrt{x-2} + \cdots + \sqrt{x-n} \lt x
$$
holds for every real number $x \ge n$.