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Supposeyou begin with apile ofnstones and split this pileintonpiles of one stone each by successively splitting apile 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 tliatiftliese piles haverandsstones in them, respectively, you computers. Show that no matter how you split the piles, the sum of the products computed at each step equalsn(n-1)/2.
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Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
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