Pre-Calc
Thursday, April 23, 2009
Section 11.7: The Principle of Mathematical Induction
Principal of Mathematical Induction:
Let S be a statement for every positive integer n.
n
If:
1. S1 is true, and
2. the truth of S implies the truth of S
for
k
k+1
every positive integer K, then Sn is true for every
positive integer n.
1
Pre-Calc
Thursday, April 23, 2009
Section 11.7: The Principle of Mathematical Induction
Steps of Mathematical Induction:
1) State (and verify): S1 : the statement for n = 1
2) State Sk : the statement for n = k
3) State Sk+1 : the statement for n = k+1
4) Show that by assuming Sk , you can conclude Sk+1
2
Pre-Calc
Thursday, April 23, 2009
Section 11.7: The Principle of Mathematical Induction
Example: Use mathematical induction to prove that the
statement
is true for every positive integer n.
3
Pre-Calc
Thursday, April 23, 2009
Section 11.7: The Principle of Mathematical Induction
Example: Use mathematical induction to prove that the
statement
is true for every positive integer n.
4