Hello,

Sorry for the "innovation", but I copied it from one of my other posts..

Also see here : Mathematical induction - Wikipedia, the free encyclopediaOk, there are three main steps in an induction proof

Preliminary : state the induction property

This is mostly for yourself, to clear out the view.

1st step: the basis.

You have to check that this is true for the very first term.

2nd step: the inductive step.

Induction hypothesis: assume that the property is true for a rank n.

Then,provethat if this is verified for a rank n, it will be for the following rank, n+1.

In most of the induction exercises, this proof will require you to go back to the recursive definition of

-----------------------------

Here, .

Basis : Prove that is true << this is easy here;

Inductive hypothesis :

Prove that is true : .

proof :

, according to the inductive hypothesis.

Factor by :

(1)

-----------------------------

On your draft paper, note that you have to prove that this is equal to , that is to say prove that

-----------------------------

So factor (1) correctly, in order to get what you want...

In fact, you should always be able to keep in mind what formula you want to prove (the P_{n+1} thing).

Is it clear enough ?