Use the Formula for the Sum of an Infinite Geometric Series
-$$\sum _ { i = 1 } ^ { \infty } 11 ( - 0.2 ) ^ { i } - 1$$
A) $\frac { 55 } { 6 }$
B) $\frac { 55 } { 4 }$
C) $- \frac { 55 } { 6 }$
D) $- \frac { 55 } { 4 }$ Express the repeating decimal as a fraction in lowest terms.

Question

Quizplus · Accepted Answer

The sum of an infinite geometric series is given by the formula:$$\sum_{i=1}^\infty ar^i = \frac{a}{1-r}$$where $a$ is the first term and $r$ is the common ratio.In this case, $a = 11$ and $r = -0.2$. So, the sum of the series is:$$\sum_{i=1}^\infty 11(-0.2)^i = \frac{11}{1-(-0.2)} = \frac{11}{1.2} = \frac{55}{6}$$Therefore, the correct answer is A.

Use the Formula for the Sum of an Infinite Geometric ∑i=1∞11(−0.2)i−1\sum _ { i = 1 } ^ { \infty } 11 ( - 0.2 ) ^ { i } - 1i=1∑∞​11(−0.2)i−1

Use the Formula for the Sum of an Infinite Geometric $\sum _ { i = 1 } ^ { \infty } 11 ( - 0.2 ) ^ { i } - 1$