This document introduces proof by induction as a strategy to prove statements for all natural numbers. It explains that proof by induction requires first proving the base case for the first natural number, then proving that if the statement holds true for an arbitrary natural number k, it also holds true for k+1. The document then presents an example statement to prove using induction: for any natural number n, the product of n, n+1, and n+2 is divisible by 3.

1. *
like climbing the ladder of natural numbers

2. 3
2
1

3. k+1
k

4. *Why use “proof by induction”?
*You use this strategy when you
want to prove something is true
FOR ALL NATURAL NUMBERS.
*

5. *First prove that you can get on the ladder.
(on the first rung) What is the first natural
number?
*Then prove that you are able to take a step
from one rung to the next. (from rung k to
rung k+1) To do this, you pretend it is true
for k and then see if you can get it to work
for k+1.
*

6. *For any n that is a natural number,
n(n+1)(n+2) is divisible by 3.
*In other words, if you take any 3
consecutive natural numbers and
multiply them together, the
product will be divisible by 3.
*Prove it!!
*