1. The number of positive integer values of $n$ that satisfy $\left|\sqrt{\frac{n}{n+2009}}-1\right|>\frac{1}{1005}$ is $\qquad$
1.1008015.

By
$$
\begin{array}{l}
1-\sqrt{\frac{n}{n+2009}}>\frac{1}{1005} \Rightarrow \sqrt{\frac{n}{n+2009}}<\frac{1004}{1005} \\
\Rightarrow \frac{n}{n+2009}<\frac{1004^2}{1005^2} \Rightarrow n<\frac{1004^2}{1005^2-1004^2} \cdot 2009=1008014.25
\end{array}
$$
Thus, the number of positive integer values of $n$ for which $1-\sqrt{\frac{n}{n+2009}}>\frac{1}{1005}$ holds is 1008015.