题目

计算 $n$ 阶行列式 ${D}_{n} = \left| \begin{matrix} {a}_{1} & {b}_{1} & 0 & \cdots & 0 & 0 \\ 0 & {a}_{2} & {b}_{2} & \cdots & 0 & 0 \\ \vdots & \vdots & \vdots & & \vdots & \vdots \\ 0 & 0 & 0 & \cdots & {a}_{n - 1} & {b}_{n - 1} \\ {b}_{n} & 0 & 0 & \cdots & 0 & {a}_{n} \end{matrix}\right| + \left| \begin{matrix} {a}_{1} & 0 & 0 & \cdots & 0 & {b}_{n} \\ {b}_{1} & {a}_{2} & 0 & \cdots & 0 & 0 \\ 0 & {b}_{2} & {a}_{3} & \cdots & 0 & 0 \\ \vdots & \vdots & \vdots & & \vdots & \vdots \\ 0 & 0 & 0 & \cdots & {a}_{n - 1} & 0 \\ 0 & 0 & 0 & \cdots & {b}_{n - 1} & {a}_{n} \end{matrix}\right|$,其中 ${a}_{i},{b}_{i}$ 均
不为
0.