证明：
$\left|\begin{array}{cccccc}
a+b & a b & 0 & \cdots & 0 & 0 \\
1 & a+b & a b & \cdots & 0 & 0 \\
0 & 1 & a+b & \cdots & 0 & 0 \\
\cdots \\
0 & 0 & 0 & \cdots & 1 & a+b
\end{array}\right|=\frac{a^{n+1}-b^{n+1}}{a-b},$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$
$\text{E.}$
$\text{F.}$