7. Given that $a$ is a positive root of the equation $x^{2}-x-2000=0$. Then the value of the algebraic expression $3+\frac{2000}{1+\frac{2000}{1+2000}}$ is $\qquad$ .
$$
=.7 . \frac{5+3 \sqrt{889}}{2}
$$

Given that $a$ is a positive root of the equation $x^{2}-x-2000=0$, we have $a^{2}-a-2000=0$, and $a=\frac{1+3 \sqrt{889}}{2}$. From $a^{2}-a-2000=0$, we get $a=1+\frac{2000}{a}$. Therefore, the original expression $=3+\frac{2000}{1+\frac{2000}{a}}=2+1+\frac{2000}{a}$ $=2+a=\frac{5+3 \sqrt{889}}{2}$.