13.7 –
Mathematical
Induction
MATHEMATICAL INDUCTION
13.7
Objectives: You should be able to…
MATH INDUCTION
Mathematical induction is a method of proof. If we prove
something is true for any particular case, then it must be true for
the next case. There are three steps used in mathematical
induction:
1. Show that statement is true for n = 1.
2. Assume the statement is true for n = k
3. Prove the statement is true for n = k + 1 using the
assumption.
EXAMPLE:
1
1
1
1
n


 ...

Prove that
1 2 2  3 3 4
n(n 1) n 1
for all positive integers n.
EXAMPLE:
Use mathematical induction to prove that the
following statement is true for all positive
integers n.
3n2  n
1 4  7  ... (3n  2) 
2