Use the Formula for the Sum of an Infinite Geometric Series
-$0 . \overline { 44 } = \frac { 44 } { 100 } + \frac { 44 } { 10,000 } + \frac { 44 } { 1,000,000 } + \ldots$
A) $\frac { 4 } { 9 }$
B) $\frac { 4444 } { 999 }$
C) $\frac { 4400 } { 999 }$
D) $\frac { 1111 } { 2500 }$

Question

Quizplus · Accepted Answer

The given series is an infinite geometric series with the first term $a = \frac{44}{100}$ and common ratio $r = \frac{1}{100}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$. Substituting the values, we get $S = \frac{\frac{44}{100}}{1 - \frac{1}{100}} = \frac{44}{100} \times \frac{100}{99} = \frac{44}{99} = \frac{4}{9}$.

Use the Formula for the Sum of an Infinite Geometric 0.44‾=44100+4410,000+441,000,000+…0 . \overline { 44 } = \frac { 44 } { 100 } + \frac { 44 } { 10,000 } + \frac { 44 } { 1,000,000 } + \ldots0.44=10044​+10,00044​+1,000,00044​+…

Use the Formula for the Sum of an Infinite Geometric $0 . \overline { 44 } = \frac { 44 } { 100 } + \frac { 44 } { 10,000 } + \frac { 44 } { 1,000,000 } + \ldots$