Find the sum of the infinite geometric series.
$$\sum _ { n = 0 } ^ { \infty } 4 \left( - \frac { 1 } { 5 } \right) ^ { n }$$
A) $- \frac { 10 } { 3 }$
B) $\frac { 10 } { 3 }$
C) $\frac { 2 } { 3 }$
D) $- \frac { 2 } { 3 }$
E) undefined

Question

Quizplus · Accepted Answer

The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, where $a$ is the first term and $r$ is the common ratio. Here, $a = 4$ and $r = -\frac{1}{5}$. Plugging these values in, we get $S = \frac{4}{1 - (-\frac{1}{5})} = \frac{4}{1 + \frac{1}{5}} = \frac{4}{\frac{6}{5}} = \frac{4 \cdot 5}{6} = \frac{20}{6} = \frac{10}{3}$.

Find the Sum of the Infinite Geometric Series ∑n=0∞4(−15)n\sum _ { n = 0 } ^ { \infty } 4 \left( - \frac { 1 } { 5 } \right) ^ { n }n=0∑∞​4(−51​)n

Find the Sum of the Infinite Geometric Series $\sum _ { n = 0 } ^ { \infty } 4 \left( - \frac { 1 } { 5 } \right) ^ { n }$