Sum of Geometric Sequence/Corollary 1

Corollary to Sum of Geometric Progression
Let $a, ar, ar^2, \ldots, ar^{n-1}$ be a geometric progression.

Then:
 * $\displaystyle \sum_{j \mathop = 0}^{n - 1} ar^j = \frac {a \left({r^n - 1}\right)} {r - 1}$

Proof
We have that $a + ar + ar^2 + \cdots + ar^{n-1}$ is exactly the same as $a \left({1 + r + r^2 + \cdots + r^{n-1}}\right)$.

The result follows from Sum of Geometric Progression.