Question 24
Does there exist an integer $a$ such that
$$
\frac{1}{\sqrt{2024}} \lt \frac{1}{\sqrt{a+1}} + \frac{1}{\sqrt{a+2}} + \dots + \frac{1}{\sqrt{a+2023}} \lt \frac{1}{\sqrt{2023}}?
$$
$$
\frac{1}{\sqrt{2024}} \lt \frac{1}{\sqrt{a+1}} + \frac{1}{\sqrt{a+2}} + \dots + \frac{1}{\sqrt{a+2023}} \lt \frac{1}{\sqrt{2023}}?
$$