IMO 1989 LL ICE40

A sequence of real numbers x0, x1, x2, . . . is defined as follows:

IMO 1989 LL ICE40

Origin: ICE

Problem

A sequence of real numbers x0, x1, x2, . . . is defined as follows: x0 = 1989 and for each n \geq1 xn = −1989 n n−1  k=0 xk. Calculate the value of 1989 n=0 2nxn.