rút gọn $\frac{1}{1-\sqrt[]{2}}-\frac{1}{\sqrt[]{2}-\sqrt[]{3}}+\frac{1}{\sqrt[]{3}-\sqrt[]{4}}-\cdots+\frac{1}{\sqrt[]{99}-\sqrt[]{100}}$

$\displaystyle  \begin{array}{{>{\displaystyle}l}}
\ \ \ \ \ \frac{1}{1-\sqrt{2}} -\frac{1}{\sqrt{2} -\sqrt{3}} +\frac{1}{\sqrt{3} -\sqrt{4}} -...+\frac{1}{\sqrt{99} -\sqrt{100}}\\
=\frac{1+\sqrt{2}}{\left( 1+\sqrt{2}\right)\left( 1-\sqrt{2}\right)} -\frac{\sqrt{2} +\sqrt{3}}{\left(\sqrt{2} -\sqrt{3}\right)\left(\sqrt{2} +\sqrt{3}\right)} +\frac{\sqrt{3} +\sqrt{4}}{\left(\sqrt{3} -\sqrt{4}\right)\left(\sqrt{3} +\sqrt{4}\right)} -...+\frac{\sqrt{99} +\sqrt{100}}{\left(\sqrt{99} -\sqrt{100}\right)\left(\sqrt{99} +\sqrt{100}\right)}\\
=\frac{1+\sqrt{2}}{-1} -\frac{\sqrt{2} +\sqrt{3}}{-1} +\frac{\sqrt{3} +\sqrt{4}}{-1} -....+\frac{\sqrt{99} +\sqrt{100}}{-1}\\
=-1-\sqrt{2} +\sqrt{2} +\sqrt{3} -\sqrt{3} -\sqrt{4} +...-\sqrt{99} -\sqrt{100}\\
=-1-\sqrt{100}\\
=-1-10\\
=-11
\end{array}$