1. Proof by Induction 1.Explanation 1Explanation 1 2.Explanation 2Explanation 2 3.Example DivisionExample Division 4.Example SequencesExample Sequences 5.Example FactorialsExample Factorials JMG©

2. Is every car in the line red? This would constitute a proof or would it? 1.Find one car that is red 2.Show that every car is the same as the one beside it These are the basic steps in the Mathematical proof by induction JMG© Menu

3. JMG© Mathematical steps Proof by induction we will apply to statements that have a sequential element It May be necessary to use a number greater than 1 on some occasions 2. Assume that the statement is true for some Natural number K 3. Using this assumption prove the statement true for k + 1 Menu

4. JMG© Proof by Induction Correct Take a bit of each! Factorise True by assumption Obviously true Therefore Menu

5. If you add n odd numbers the answer is n 2 Correct This is the nth odd number Assume true for k that is Consider the k + 1 case Add the same thing to both sides Quid erat demonstrandumThe proposition is proved Menu JMG©

6. Note here, the statement is only true when n is at least 5 Correct Assume true for k and consider for k + 1 Is true Which means So it must be true for k + 1 Menu JMG©