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 $p$ is a real number, $p \neq 1$ .
$S _ { n } : 1 + p + p ^ { 2 } + \ldots + p ^ { n }$

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