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

question 134

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) \(\quad \mathrm { r } ^ { n + 1 } - 1\)
• C) \(\quad \frac { r ^ { n + 1 } } { r - 1 }\)
• D) \(\quad \frac { 1 - r ^ { n } } { 1 - r }\)
• E) \(\quad \frac { 1 - r ^ { n } } { 1 - r ^ { n - 1 } }\)

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