Sum of Geometric Sequence/Corollary 1/Proof 1

Proof
By Multiplication of Numbers Distributes over Addition
 * $a + a r + a r^2 + \cdots + a r^{n - 1} = a \left({1 + r + r^2 + \cdots + r^{n - 1} }\right)$

The result follows from Sum of Geometric Progression.