Show that for any number and real number that

.

My attempt at a proof is that we should argue by induction, taking as a base case, which is easy to show:

So now let's assume that . Then:

And it's finding out what that fraction is going to be over (as I know that sum is not just 1 due to the terms that will be in the bottom. I think once I figure that one out the proof should fall out nicely (unless of course I'm making it way too hard and it's easier to prove directly).