11. Let $a_{n}$ be the coefficient of $x$ in the binomial expansion of $(3-\sqrt{x})^{n}(n=2,3, \cdots)$. Then
$$
\sum_{n=2}^{18} \frac{3^{n}}{a_{n}}=
$$
$\qquad$
11. 17.

Since $a_{n}=3^{n-2} C_{n}^{2}$, therefore,
$$
\frac{3^{n}}{a_{n}}=3^{2} \times \frac{2}{n(n-1)}=\frac{18}{n(n-1)} \text {. }
$$

Thus, $\sum_{n=2}^{18} \frac{3^{n}}{a_{n}}=18 \sum_{n=2}^{18} \frac{1}{n(n-1)}=17$.