In duction follows a pattern:Originally Posted bycen0te

1. First we show that what we wish to prove for general

n actualy holds for the first n which is realevant to the

problem. In this case it's n=0, and we need to show that

for every x>0 that:

,which I presume you know is true.

2. Second we show that if what we have to prove is true

when n=k, then it is also true for n=k+1. So assume it

true for n=y, then we have

,

for all .

Now consider:

also:

Now the integrand in [1] is strictly greater than the integrand in

[2] at every point over which the integral is taken. So

which can be rewritten from what we have found above as:

So rearranging and replacing y by x we have:

3. That is we have proven that if what we have to prove for all ,

is true for n=k, then it is true for n=k+1, also we have proven that

it is true for n=0, so by the principle of induction we have proven

it true for all

RonL