(x^k) - 1 = (x - 1)*(x^(k-1) + x^(k-2) + ... + x + 1)

*Dickfore*

Use mathematical induction:
[tex]
x^{k+1} - 1 = (x^{k+1} - x^k) + (x^k - 1) = (x - 1) x^k +(x^k - 1)
[/tex]

Dickfore	Use mathematical induction: [tex] x^{k+1} - 1 = (x^{k+1} - x^k) + (x^k - 1) = (x - 1) x^k +(x^k - 1) [/tex]