Melilla 2018-P5

Calcular el valor del determinante $$\begin{vmatrix} \frac{1}{1!} & 1 & 0 & 0 & \dots & 0 \\ \frac{1}{2!} & \frac{1}{1!} & 1 & 0 & \dots & 0 \\ \frac{1}{3!} & \frac{1}{2!} & \frac{1}{1!} & 1 & \dots & 0 \\ \frac{1}{4!} & \frac{1}{3!} & \frac{1}{2!} & \frac{1}{1!} & \dots & 0 \\ \vdots...