Provide an appropriate response.
-Convert the decimal $.340340340$. . to a fraction by writing it as the infinite series $\frac { 340 } { 1000 } + \frac { 340 } { 1000 ^ { 2 } } + \frac { 340 } { 1000 ^ { 3 } } + \ldots$
A) $0.339$
B) $0.34134134$
C) $\frac { 340 } { 999 }$
D) $0.341$

Question

Quizplus · Accepted Answer

The given decimal can be expressed as an infinite geometric series with the first term $a = \frac{340}{1000}$ and common ratio $r = \frac{1}{1000}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$. Substituting the values of $a$ and $r$, we get $S = \frac{\frac{340}{1000}}{1 - \frac{1}{1000}} = \frac{340}{999}$, which simplifies to option C.

Provide an Appropriate Response .340340340.340340340.340340340 to a Fraction by Writing It as the Infinite

Provide an Appropriate Response $.340340340$ to a Fraction by Writing It as the Infinite