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Unformatted text preview: 2! + ... + n n ! = ( n + 1)!-1 whenever n is a positive integer. 8 (3 points) Use mathematical induction to prove that 1 2 3+2 3 4+ ... + n ( n +1) ( n +2) = n ( n +1)( n +2)( n +3) / 4 9 (4 points) Use mathematical induction to prove that a set with n elements has n ( n-1)( n-2) / 6 subsets containing exactly three elements whenever n is an integer greater than or equal to 3 10 (5 points) Find the aw with the following proof that a n = 1 for all nonnegative integers n , whenever a is a nonzero real number. Basic Step : a = 1 is true by the denition of a . Inductive Step : Assume that a k = 1 for all nonnegative integers k with k n . Then note that a n +1 = a n a n a n-1 = 1 1 1 = 1 11 (15 points) Prove that for any integer n a 2 n 2 n grid with one corner square removed can be covered with L shaped tiles made up of 3 squares. 2...
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- Fall '09