20. $\left(1-\frac{1}{2^{2}}\right)\left(1-\frac{1}{3^{2}}\right)\left(1-\frac{1}{4^{2}}\right) \cdots\left(1-\frac{1}{2003^{2}}\right)$'s value is ( ).
(A) $\frac{2005}{4006}$
(B) $\frac{1001}{2003}$
(C) $\frac{1}{2}$
(D) $\frac{1002}{2003}$
(E) $\frac{2007}{4006}$
20.D.
$$
\begin{array}{l}
\text { Original expression }=\frac{1 \times 3}{2^{2}} \times \frac{2 \times 4}{3^{2}} \times \cdots \times \frac{2001 \times 2003}{2002^{2}} \times \frac{2002 \times 2004}{2003^{2}} \\
=\frac{2004}{2 \times 2003}=\frac{1002}{2003} .
\end{array}
$$