试证
$$
D_n=\left|\begin{array}{cccccc}
x & -1 & 0 & \cdots & 0 & 0 \\
0 & x & -1 & \cdots & 0 & 0 \\
0 & 0 & x & \cdots & 0 & 0 \\
\vdots & \vdots & \vdots & & \vdots & \vdots \\
0 & 0 & 0 & \cdots & x & -1 \\
a_n & a_{n-1} & a_{n-2} & \cdots & a_2 & a_1+x
\end{array}\right| \text {. } \begin{gathered}
\\
=x^n+a_1 x^{n-1}+a_2 x^{n-2}+\cdots+a_{n-1} x+a_n \quad(n \geqslant 2) .
\end{gathered}
$$