2. $\frac{1}{2002}+\frac{1}{3.003}-\frac{1}{4004}+\frac{1}{6006}-\frac{1}{8008}$ $=(\quad)$.
(A) $\frac{1}{6006}$
(B) $-\frac{3}{7007}$
(C) $\frac{5}{8008}$
(D) $-\frac{7}{9009}$
Prompt: Transform the denominator of each fraction to
$$
\begin{array}{l}
2 \times 1001, 3 \times 1001, 4 \times 1001, \\
6 \times 1001, 8 \times 1001 .
\end{array}
$$

Answer: $\frac{5}{8008}$.