So the first bit of the question gives you the approximation...
...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.
Therefore it was not you who failed (to understand) but me who failed to read your question correctly.