So the first bit of the question gives you the approximation...

with and

...to find the approximate value of , which I've done.

The the second part is...

The Extended Mean Value Theorem says that for fixed , and , there is a in the range , such that

Use this to show that for some with we have

...which I think I've managed okay, but it's this next bit that I'm stuck on...

Deduce more generally that

...for some integers and numbers where .

Can anyone help? I just can't get my head around it.