Provide an appropriate response.
-Convert the decimal .959595... to a fraction by writing it as the infinite series $\frac { 95 } { 100 } + \frac { 95 } { 100 ^ { 2 } } + \frac { 95 } { 100 ^ { 3 } } + \ldots$
A) $\frac { 95 } { 99 }$
B) $0.94$
C) $0.96969697$
D) $0.96$

Question

Quizplus · Accepted Answer

This decimal is a repeating decimal, which can be represented as an infinite geometric series with the first term $a = \frac{95}{100}$ and common ratio $r = \frac{1}{100}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$. Substituting $a = \frac{95}{100}$ and $r = \frac{1}{100}$ gives $S = \frac{\frac{95}{100}}{1 - \frac{1}{100}} = \frac{95}{99}$, which matches choice A.

Provide an Appropriate Response 95100+951002+951003+…\frac { 95 } { 100 } + \frac { 95 } { 100 ^ { 2 } } + \frac { 95 } { 100 ^ { 3 } } + \ldots10095​+100295​+100395​+…

Provide an Appropriate Response $\frac { 95 } { 100 } + \frac { 95 } { 100 ^ { 2 } } + \frac { 95 } { 100 ^ { 3 } } + \ldots$