$ \begin{aligned}解：原式&=(2 \sqrt{2024}+2)×(\frac{\sqrt{2}-1}{2}+\frac{\sqrt{3}-\sqrt{2}}{2}+ \frac{2-\sqrt{3}}{2}+···+\frac{\sqrt{2024}-\sqrt{2023}}{2}) \\ &=2( \sqrt{2024}+1)×\frac{\sqrt{2024}-1}{2} \\ &=( \sqrt{2024}+1)×( \sqrt{2024}-1) \\ &=2024-1 \\ &=2023 \\ \end{aligned}$
