11. Let $a_{n}$ be the coefficient of $x$ in the binomial expansion of $(3-\sqrt{x})^{n}(n=2,3, \cdots)$. Then the value of $\frac{3^{2}}{a_{2}}+\frac{3^{3}}{a_{3}}+\cdots+\frac{3^{18}}{a_{18}}$ is . $\qquad$
$$
\begin{array}{l}
\text { Since } a_{n}=\mathrm{C}_{n}^{2} \cdot 3^{n-2}, \text { then, } \\
\frac{3^{n}}{a_{n}}=\frac{3^{n}}{\mathrm{C}_{n}^{2} \cdot 3^{n-2}}=3^{2} \times \frac{2}{n(n-1)}=\frac{18}{n(n-1)} . \\
\text { Therefore, } \frac{3^{2}}{a_{2}}+\frac{3^{3}}{a_{3}}+\cdots+\frac{3^{18}}{a_{18}} \\
=18\left(\frac{1}{2 \times 1}+\frac{1}{3 \times 2}+\cdots+\frac{1}{18 \times 17}\right) \\
=18\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\cdots+\frac{1}{17}-\frac{1}{18}\right)=17 .
\end{array}
$$