If \(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\ldots +\frac{1}{\sqrt{99}+\sqrt{100}}=m\) and \(\frac{1}{1…

If \(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\ldots +\frac{1}{\sqrt{99}+\sqrt{100}}=m\) and \(\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\ldots +\frac{1}{99\cdot 100}=n\), then the point \((m, n)\) lies on the line

[JEE Main 2024, 5 Apr (Shift 1)]