Mathematical Induction
We use Mathematical Induction to prove the truth of a statement. It can be used to prove simple
mathematical identities like
∑
N
i
=1
i
=
N
(
N
+1)
2
to statements like the ”A polygon has many sides as it has angles”. In general the statement is
made on some property that applies to natural numbers (for example
N
in the above example).
The steps involved in a proof by Mathematical induction are:
Step 1: Basis
Show that the statement is true for some base cases, say N=1, 2 etc.
Step 2: Inductive Hypothesis
Assume that the statement is true for some natural number
N
=
k
.
Step 3: Inductive Step
Using the inductive hypothesis prove that the statement is true for
N
=
k
+ 1 as well.
We will take two examples of Mathematical Induction
On Fibonacci Numbers
Lets prove the following statement by following the process of Mathematical Induction:
The sum of the ﬁrst N odd Fibonacci numbers is equal to the (2N)th Fibonacci number
The given statement can be written as:
F
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 NETTLES
 Mathematical Induction, Natural number, Peano axioms, complete binary tree

Click to edit the document details