We will prove, by induction that for all that the statement :

is true.

First when the left hand side is , and the right hand side is

, so it is true for

Now suppose that for some that the holds, then:

but by supposition the square bracket is equal to:

,

so:

Which is .

To summarise, we have shown that is true, and that if is true then so is , so in short we

have proven by mathematical induction that holds for all

RonL