Select the Right Expression for the Following Sum and Prove $n$

Multiple Choice

Select the right expression for the following sum and prove your statement is true for all natural numbers $n$ , where $r$ is a real number, $r \neq 1$ .
$S _ { n } : 1 + r + r ^ { 2 } + \ldots + r ^ { n }$

A) $\quad \frac { 1 - r ^ { n + 1 } } { 1 - r }$
B) $\quad r ^ { n + 1 } - 1$
C) $\quad \frac { r ^ { n + 1 } } { r - 1 }$
D) $\quad \frac { 1 - r ^ { n } } { 1 - r }$
E) $\quad \frac { 1 - r ^ { n } } { 1 - r ^ { n - 1 } }$