Use the Formula for the Sum of an Infinite Geometric Series
-$$\sum _ { i = 1 } ^ { \infty } 10 ( - 0.2 ) ^ { \mathrm { i } - 1 }$$
A) $\frac { 25 } { 3 }$
B) $\frac { 25 } { 2 }$
C) $- \frac { 25 } { 3 }$
D) $- \frac { 25 } { 2 }$

Question

Quizplus · Accepted Answer

The formula for the sum of an infinite geometric series is $\frac{a}{1 - r}$, where $a$ is the first term and $r$ is the common ratio. Here, $a = 10$ and $r = -0.2$. Plugging these values into the formula gives $\frac{10}{1 - (-0.2)} = \frac{10}{1.2} = \frac{25}{3}$.

Use the Formula for the Sum of an Infinite Geometric ∑i=1∞10(−0.2)i−1\sum _ { i = 1 } ^ { \infty } 10 ( - 0.2 ) ^ { \mathrm { i } - 1 }i=1∑∞​10(−0.2)i−1

Use the Formula for the Sum of an Infinite Geometric $\sum _ { i = 1 } ^ { \infty } 10 ( - 0.2 ) ^ { \mathrm { i } - 1 }$