I'm having a bit of a mental lockup on a simple sum-problem, but perhaps someone here could just give a hint as to what I'm missing.

$\displaystyle x^n-1 + x^{n-2}y + x^{n-3}y^2 +... + xy^{n-2} + y^{n-1}$

I'm not really new to sums and their formulaes, my real problem here is that I can't seem to get the quotient for the sum; it reverses so to speak:

$\displaystyle {x^{n-2}y}/x^{n-1}$ and $\displaystyle y^{n-1}/xy^{n-2}$

and I'm not sure what to do with that. I'm not after a complete solution, just a hint or two so I can figure it out!