1. Proof by Induction L.O. All pupils understand proof by induction
All pupils can use induction to prove some situations
Some pupils can use induction to prove harder identities

2. Example 1:

3. Example 1:
Step 1: show it is true when n=1

4. Step 2: assume it is true when n=k
Example 1:
Step 1: show it is true when n=1
Step 2: assume it is true when n=k

5. Step 3: using steps 1 & 2, show it is true for n=k+1
Example 1:
Step 1: show it is true when n=1
Step 2: assume it is true when n=k
Step 3: using steps 1 & 2, show it is true for n=k+1

6. Example 1: Conclude: Step 1: show it is true when n=1
Step 2: assume it is true when n=k
Step 3: using steps 1 & 2, show it is true for n=k+1
Conclude:

7. Example 2:

8. Example 2:
Step 1: show it is true when n=1

9. Step 2: assume it is true when n=k
Example 2:
Step 1: show it is true when n=1
Step 2: assume it is true when n=k

10. Step 3: using steps 1 & 2, show it is true for n=k+1
Example 2:
Step 1: show it is true when n=1
Step 2: assume it is true when n=k
Step 3: using steps 1 & 2, show it is true for n=k+1

11. Example 2: Conclude: Step 1: show it is true when n=1
Step 2: assume it is true when n=k
Step 3: using steps 1 & 2, show it is true for n=k+1
Conclude:

12. Questions: Step 1: show it is true when n=1
Step 2: assume it is true when n=k
Step 3: using steps 1 & 2, show it is true for n=k+1
Conclude:

13. Proof by Induction L.O. All pupils understand proof by induction
All pupils can use induction to prove some situations
Some pupils can use induction to prove harder identities