1. Given $a_{n}=\frac{1}{n \sqrt{n+1}+(n+1) \sqrt{n}}$. Then $a_{1}+a_{2}+\cdots+a_{99}=$ $\qquad$
$(2008$, Shanghai Jiao Tong University Winter Camp)
$$
\begin{array}{l}
\text { Hint: } a_{n}=\frac{1}{\sqrt{n} \sqrt{n+1}(\sqrt{n}+\sqrt{n+1})} \\
=\frac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n} \sqrt{n+1}}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}} .
\end{array}
$$

Answer: $\frac{9}{10}$.