Provide an appropriate response.
-Convert the decimal $.868686 \ldots$ to a fraction by writing it as the infinite series
$$\frac { 86 } { 100 } + \frac { 86 } { 100 ^ { 2 } } + \frac { 86 } { 100 ^ { 3 } } + \ldots$$
A) $0.87878788$
B) $0.87$
C) $\frac { 86 } { 99 }$
D) $0.85$

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = \frac{86}{100}$ and common ratio $r = \frac{1}{100}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$. Substituting $a = \frac{86}{100}$ and $r = \frac{1}{100}$ gives $S = \frac{\frac{86}{100}}{1 - \frac{1}{100}} = \frac{86}{99}$, which matches option C.

Provide an Appropriate Response .868686….868686 \ldots.868686… To a Fraction by Writing It as the Infinite Series

Provide an Appropriate Response $.868686 \ldots$ To a Fraction by Writing It as the Infinite Series