证明
$$
D_n=\left|\begin{array}{cccccc}
2 & -1 & & \cdots & 0 & 0 \\
-1 & 2 & -1 & \cdots & 0 & 0 \\
& -1 & 2 & \cdots & 0 & 0 \\
\vdots & \vdots & \vdots & & \vdots & \vdots \\
0 & 0 & 0 & \cdots & 2 & -1 \\
0 & 0 & 0 & \cdots & -1 & 2
\end{array}\right|=n+1
$$