Find the determinant of the AR(1) matrix given by: $$R = \begin{pmatrix} 1 & \rho & \cdots & \rho^{d-1}\\ \rho & 1 & \cdots & \rho^{d-2}\\ \vdots & \vdots & \ddots & \vdots\\ \rho^{d-1} & \rho^{d-2} & \cdots & 1 \end{pmatrix}$$
This is a common question but I want a simpler method of computation that is without using results of determinants of tridiagonal matrices. Please help!