Assume you start with the pile of n stones and split the pile into n piles of one stone each by successively splitting the pile of stones into 2 smaller piles. Every time you split the pile you multiply number of stones in each of two smaller piles you form, so that if the piles have r and s stones in them, respectively, you computers. Illustrate that no matter how you split piles, sum of products evaluated at every step equals n(n . 1)/2.