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 r and s stones in them, respectively, you compute r s . show that no matter how you split the piles, the sum of the products computed at each step equals n(n - 1)/2. (hint: use induction)