2. For a sequence $P=\left(p_{1}, p_{2}\right.$, $\cdots, p_{n}$ ), the "Cesàro sum" of $P$ (Cesàro is a mathematician) is defined as $\frac{S_{1}+S_{2}+\cdots+S_{n}}{n}$, where,
$$
S_{k}=p_{1}+p_{2}+\cdots+p_{k}(1 \leqslant k \leqslant n) .
$$

If the Cesàro sum of the sequence $\left(p_{1}, p_{2}, \cdots, p_{2006}\right)$ is 2007, then the Cesàro sum of the sequence $\left(1, p_{1}, p_{2}, \cdots, p_{2006}\right)$ is ( ).
(A) 2007
(B) 2008
(C) 2006
(D) 1004
2.A.

Let $S_{k}^{\prime}=1+p_{1}+p_{2}+\cdots+p_{k-1}=1+S_{k-1}$, then
$$
\begin{array}{l}
\frac{\sum_{k=1}^{2007} S_{k}^{\prime}}{2007}=\frac{2007+\sum_{k=1}^{2006} S_{k}}{2007} \\
=\frac{2007+2007 \times 2006}{2007}=2007 .
\end{array}
$$