I have to be honest, I hadn't looked that far down - I was trusting when mqb said "top right seems to be along the right lines".
So, have you shown the result - um,
maybe? You haven't actually "closed the gap"; you haven't even explictly said "this equals the expression in square brackets" (or words to that effect).
I'll be blunt: you
really need to think a bit more about how you want to present your work. You're consistently on that fine line where an examiner might be able to work out what you meant and if it you actually knew how to prove the result, but they might easily decide "actually, with the amount of gaps I'm filling in myself I'm basically proving this
for Student 999 - that's not OK".
It's often also just hard to puzzle out what you mean: the stuff you write e to work out what you meant, but it's going to take them ages, and if you're unlucky they're just not going to bother. I mean, look at your first line:
nxnln(xn1) where n≥0 where x0=0 My immediate reaction is WTF is x_n? And even if I knew what x_n is, why have you written this expression down? And why has a sum appeared in the next line?
Oh God. I've just realised - you actually wrote this as a LH column going down to the bottom of the page, then restarted in the RH even though your LH column is (a lot) wider than where you started your RH column. I've been reading this in the wrong frickin' order.
So I think I'm going to stop at that point - obviously my initial comment about "closing the gap" is invalid.
But the fact that a seasoned mathematician can look at your post and not be able to tell the correct order in which you've laid out your argument speaks for itself.