（华中师范大学，1994 年）计算 $n+1$ 阶行列式

$$
D_{n+1}=\left|\begin{array}{cccccc}
a & -1 & 0 & \cdots & 0 & 0 \\
a x & a & -1 & \cdots & 0 & 0 \\
a x^2 & a x & a & \cdots & 0 & 0 \\
\vdots & \vdots & \vdots & & \vdots & \vdots \\
a x^{n-1} & a x^{n-2} & a x^{n-3} & \cdots & a & -1 \\
a x^n & a x^{n-1} & a x^{n-2} & \cdots & a x & a
\end{array}\right| .
$$