3. 29 For a natural number $n \geqslant 3$. In the plane, a line $l$ is given, on which there are $n$ distinct points $p_{1}, p_{2}, \cdots, p_{n}$ in sequence. The product of the distances from point $p_{1}$ to the other $n-1$ points is denoted as $d_{i}(i=1,2, \cdots, n)$. There is also a point $Q$ in the plane not on $l$, and the distance from point $Q$ to point $p_{i}$ is denoted as $C_{i}(i=1,2, \cdots, n)$. Find the value of the following sum:
$$S_{n}=\sum_{i=1}^{n}(-1)^{n-i} \frac{C_{i}^{2}}{d_{i}}$$
[Solution] Without loss of generality, let these $n$ points be on the real axis, with coordinates $p_{i}\left(x_{i}, 0\right)(i=1,2, \cdots, n), x_{1}3 \text { when } .
\end{array}\right.$$

Substituting into (1), we get
$$S_{n}=\left(\alpha^{2}+\beta^{2}\right) T_{0}-2 \alpha T_{1}+T_{2}=T_{2}=\left\{\begin{array}{l}
1, n=3 \text { when, } \\
0, n>3 \text { when. }
\end{array}\right.$$