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

Example 1:

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

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

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

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:

Example 2:

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

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

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

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:

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:

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