This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ( n1)( n2) / 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 n1 = 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...
View Full
Document
 Fall '09

Click to edit the document details