$\text { Write the repeating decimal } 0 . \overline { 75 } \text { as a geometric series. }$
A) $\sum _ { n = 0 } ^ { \infty } 75 \left( \frac { 1 } { 100 } \right) ^ { n }$

B) $\sum _ { n = 0 } ^ { \infty } \left( \frac { 75 } { 10 } \right) ^ { n }$

C)$\sum _ { n = 0 } ^ { \infty } \frac { 75 } { 100 } \left( \frac { 1 } { 100 } \right) ^ { n }$

D)
$\sum _ { n = 0 } ^ { \infty } \frac { 75 } { 100 } - \left( \frac { 1 } { 100 } \right) ^ { n }$

E)
$\sum _ { n = 0 } ^ { \infty } \frac { 75 } { 100 } + \left( \frac { 1 } { 100 } \right) ^ { n }$

Question

$\text { Write the repeating decimal } 0 . \overline { 75 } \text { as a geometric series. }$ 
A) $\sum _ { n = 0 } ^ { \infty } 75 \left( \frac { 1 } { 100 } \right) ^ { n }$

B) $\sum _ { n = 0 } ^ { \infty } \left( \frac { 75 } { 10 } \right) ^ { n }$

C)$\sum _ { n = 0 } ^ { \infty } \frac { 75 } { 100 } \left( \frac { 1 } { 100 } \right) ^ { n }$

D)
$\sum _ { n = 0 } ^ { \infty } \frac { 75 } { 100 } - \left( \frac { 1 } { 100 } \right) ^ { n }$

E)
$\sum _ { n = 0 } ^ { \infty } \frac { 75 } { 100 } + \left( \frac { 1 } { 100 } \right) ^ { n }$

Quizplus · Accepted Answer

To write the repeating decimal $0.\overline{75}$ as a geometric series, we first note that this can be written as $$0.\overline{75}=\frac{75}{100}+\frac{75}{10000}+\frac{75}{1000000}+\cdots$$
 which means that the common ratio between consecutive terms is $\frac{1}{100}$ and the first term is $\frac{75}{100}$.
Therefore, the series can be written as $$\sum_{n=0}^{\infty}\frac{75}{100}\left(\frac{1}{100}\right)^n$$ which is equivalent to (C).

Write the repeating decimal 0.75‾ as a geometric series. \text { Write the repeating decimal } 0 . \overline { 75 } \text { as a geometric series. } Write the repeating decimal 0.75 as a geometric series.

$\text { Write the repeating decimal } 0 . \overline { 75 } \text { as a geometric series. }$