jmc

By the geometric series formula, $1+7+7^2+\cdots +7^{2004}=\frac{7^{2005}-1}{7-1}=\frac{7^{2005}-1}{6}$. Since $\phi (1000)=400$, by Fermat-Euler's Theorem, this is equivalent to finding $\frac{7^{400\cdot 5+5}-1}{6}\equiv \frac{7^5-1}{6}\equiv \boxed{801}(\mathrm{mod}1000)$.