Sum of Geometric Sequence/Corollary 1

Corollary to Sum of Geometric Sequence
Let $a, a r, a r^2, \ldots, a r^{n-1}$ be a geometric sequence.

Then:
 * $\displaystyle \sum_{j \mathop = 0}^{n - 1} a r^j = \frac {a \paren {r^n - 1} } {r - 1}$

Also presented as
This result is also seen presented as:
 * $\displaystyle \sum_{j \mathop = 0}^{n - 1} a r^j = \frac {a \paren {1 - r^n} } {1 - r}$

which is usually more manageable when $r < 1$.