3. Given $f(x)=\frac{1}{2^{x}+\sqrt{2}}$. Then
$$
\begin{array}{l}
f(-2003)+f(-2002)+\cdots+f(-1)+ \\
f(0)+f(1)+\cdots+f(2003)+f(2004) \\
=
\end{array}
$$
$3.1002 \sqrt{2}$.
Using $f(x)+f(1-x)=\frac{\sqrt{2}}{2}$, we get the result