Derivation of the Finite Geometric Series Formula

If \[S = \sum_{i=0}^{N} x^i \]

Prove:

1) \[xS = \sum_{i=1}^{N+1} x^i \] 2) \[S - xS = 1 - x^{N+1} \] 3) \[S = (1 - x^{N+1})/(1 - x) \]