I don't need help with induction but just part of the question.

Prove for any real x and for all n > 1

that $\displaystyle x^n-1=(x-1)(x^{n-1}+x^{n-1}+\cdots +x^{n-r}+\cdots +x+1)$

It isn't stated but is n supposed to be Naturals or Integers? Or is n in Reals?