SE-SKOLORNAS 1966 Problem 2

$a_1 + a_2 + ... + a_n = 0$ , for some $k$ we have $a_j \le 0$ for $j \le k$ and $a_j \ge 0$ for $j > k$ . If ai are not all $0$ , show that $a_1 + 2a_2 + 3a_3 + ... + na_n > 0$ .