1.2.10 Determinant calculation
Problem:
Calculate the determinant \( \Delta_{n} \) of size \( n \times n \).
\[
\Delta_{n}=\left|\begin{array}{ccccc}
x & y & 0 & \cdots & 0 \\
0 & x & y & \cdots & 0 \\
0 & 0 & x & \cdots & 0 \\
\cdots & \cdots & \cdots & \cdots & \cdots \\
y & 0 & 0 & \cdots & x
\end{array}\right| \text {. }
\]