3. Calculate $\frac{1}{1 \times 3 \times 5}+\frac{1}{3 \times 5 \times 7}+\frac{1}{5 \times 7 \times 9}+\cdots+\frac{1}{2001 \times 2003 \times 2005}$.
3.【Solution】Original expression $=$
$$
\begin{array}{l}
\frac{1}{4} \times\left\{\left(\frac{1}{1 \times 3}-\frac{1}{3 \times 5}\right)+\left(\frac{1}{3 \times 5}-\frac{1}{5 \times 7}\right)+\cdots+\left(\frac{1}{2001 \times 2003}-\frac{1}{2003 \times 2005}\right)\right\} \\
=\frac{1}{4} \times\left(\frac{1}{1 \times 3}-\frac{1}{2003 \times 2005}\right)=\frac{1004003}{12048045}
\end{array}
$$