$\frac{1}{2\sqrt{1}+\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+\cdots +\frac{1}{25\sqrt{24}+24\sqrt{25}}=$＿＿＿＿＿．