3. $\frac{C_{2002}^{0}}{1}+\frac{C_{2002}^{1}}{2}+\frac{C_{2002}^{3}}{3}+\cdots \cdots+\frac{C_{2002}^{2001}}{2002}+\frac{C_{2002}^{202}}{2003}$ The value is $(）$.
A. $\frac{2^{2003}-1}{2003}$
H. $\frac{2^{2003}}{2003}$
C. $\frac{2^{2002}+1}{2002}$
D. $\frac{2^{2003}+1}{2002}$
$$
\begin{array}{l}
\frac{C_{50 \times 22}}{k+1}=\frac{2002!}{k!(2002-k)!} \cdot \frac{1}{k+1}=\frac{2002!}{(k+1)!(2002-k)!} \cdot \frac{1}{2003} \\
=\frac{1}{2003} C_{2003}^{11}(k=0,1,2 \cdots, 2002) \\
\text { and }(x+1)^{2003}=C_{2003}^{1}+C_{2003}^{1} \cdot x^{1}+C_{2003}^{2} \cdot x^{2} \cdots+C_{2003}^{2003} \cdot x^{2003} \text {, taking } x=1 \text { we have: } \\
C_{2003}^{1}+C_{2003}^{2} \cdots+C_{2003}^{2003}=2^{2003}-1 \text {, thus the required expression }=\frac{2^{2003}-1}{2003} \\
\end{array}
$$