ILL 1987 Problem 36

A game consists in pushing a flat stone along a sequence of squares $S_0, S_1, S_2, . . .$ that are arranged in linear order. The stone is initially placed on square $S_0$ . When the stone stops on a square $S_k$ it is pushed again in the same direction and so on until it reaches $S_{1987}$ or goes beyond it; then the game stops. Each time the stone is pushed, the probability that it will advance exactly $n$ squares is $\frac{1}{2^n}$ . Determine the probability that the stone will stop exactly on square $S_{1987}.$