
1.2.9 Determinant calculation
Problem:
Calcualte the determinant of \( n \)-th order
\[
\Delta_{n}=\left|\begin{array}{cccccc}
a+b & a b & 0 & \ldots & 0 & 0 \\
2 & a+b & a b & \ldots & 0 & 0 \\
0 & 1 & a+b & \ldots & 0 & 0 \\
\ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\
0 & 0 & \ldots & \ldots & a+b & a b \\
0 & 0 & \ldots & \ldots & 1 & a+b
\end{array}\right| .
\]