Find the sum of the infinite geometric series.? $$\sum _ { n = 0 } ^ { \infty } \left( - \frac { 1 } { 8 } \right) ^ { n }$$ ?
A) $\frac { 8 } { 9 }$
B) $- \frac { 8 } { 9 }$
C) $- \frac { 9 } { 8 }$
D) $\frac { 9 } { 10 }$
E) $\frac { 9 } { 8 }$

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, $a = 1$ (since $(- \frac{1}{8})^0 = 1$) and $r = -\frac{1}{8}$. Plugging these values into the formula gives $S = \frac{1}{1 - (-\frac{1}{8})} = \frac{1}{1 + \frac{1}{8}} = \frac{1}{\frac{9}{8}} = \frac{8}{9}$.

Find the Sum of the Infinite Geometric Series ∑n=0∞(−18)n\sum _ { n = 0 } ^ { \infty } \left( - \frac { 1 } { 8 } \right) ^ { n }n=0∑∞​(−81​)n

Find the Sum of the Infinite Geometric Series $\sum _ { n = 0 } ^ { \infty } \left( - \frac { 1 } { 8 } \right) ^ { n }$