\(A=\frac{1}{\sqrt{1}+\sqrt{2}}+...+\frac{1}{\sqrt{n-1}+\sqrt{n}}\)
\(=\frac{\sqrt{1}-\sqrt{2}}{1-2}+...+\frac{\sqrt{n-1}-\sqrt{n}}{n-1-n}\)
\(=\frac{\sqrt{1}-\sqrt{2}+\sqrt{2}-\sqrt{3}+...+\sqrt{n-1}-\sqrt{n}}{-1}\)
\(=\frac{1-\sqrt{n}}{-1}=\sqrt{n}-1\)
Vậy \(A=\sqrt{n}-1\)