Suppose you begin with a pile of n stones and split this pile into n piles of one stone each by successively splitting a pile of stones into two smaller piles. Each time you split a pile you multiply the number of stones in each of the two smaller piles you form, so that if these piles have rand s stones in them, respectively, you compute rs. Show that no matter how you spilt the piles, the sum of the products computed at each step equals n(n-1)/2