9.6 Mathematical Induction
Name: ____________________
Objectives: Students will be able to use the principle of
mathematical induction to prove mathematical generalizations.
1.) BASE STEP:
This typically means to show the statement is true for n = 0 or n = 1.
2.) INDUCTIVE HYPOTHESIS:
Assume the statement is true for n = k.
3.) INDUCTIVE STEP:
Show the statement is true for n = k + 1.
Mar 19­8:25 PM
Prove that 1 + 3 + 5 + ... + (2n -1) = n2 is true for all positive
integers n.
Mar 19­8:34 PM
1
Prove that 12 + 22 + 32 + ... + n2 = [n(n+1)(2n+1)]/6 is true for all
positive integers n.
Mar 19­8:35 PM
Prove that 6 is a factor of 7n - 1 for all positive integers n.
Mar 19­8:37 PM
2
Prove that Ʃ k3 = n2(n+1)2 is true for all positive integers.
4
Mar 19­8:38 PM
Prove that the minimum number
of moves required to move a stack
of n washers in a Tower of Hanoi
game is 2n - 1.
Mar 19­8:40 PM
3
Assignment: Page 756 #1, 3, 13-16, 19, 23
Mar 19­8:41 PM
4