RIOPLATENSE 1997 Problem 5

Let $x_1, x_2, ... , x_n$ be non-negative numbers $n\ge3$ such that $x_1 + x_2 + ... + x_n = 1$ . Determine the maximum possible value of the expression $x_1x_2 + x_2x_3 + ... + x_{n-1}x_n$ .