ISL 1989 Problem 38

A sequence of real numbers $x_0, x_1, x_2, \ldots$ is defined as follows: $x_0 = 1989$ and for each $n \geq 1$

$$x_n = - \frac{1989}{n} \sum^{n-1}_{k=0} x_k.$$

Calculate the value of $\sum^{1989}_{n=0} 2^n x_n.$