Ta có : \(\frac{1}{\sqrt{n}-\sqrt{n+1}}=\frac{\sqrt{n+1}+\sqrt{n}}{\left(\sqrt{n}+\sqrt{n+1}\right)\left(\sqrt{n}-\sqrt{n+1}\right)}=-\left(\sqrt{n+1}+\sqrt{n}\right)\) với \(n\in N^{\text{*}}\)
Áp dụng : \(\frac{1}{\sqrt{1}-\sqrt{2}}+\frac{1}{\sqrt{2}-\sqrt{3}}+...+\frac{1}{\sqrt{24}-\sqrt{25}}=-\left(\sqrt{1}+\sqrt{2}+\sqrt{2}+\sqrt{3}+...+\sqrt{24}+\sqrt{25}\right)\)