Find the sum of the series.
-$$\sum _ { n = 8 } ^ { \infty } \frac { 1 } { 3 ^ { n } }$$
A) $\frac { 2187 } { 2 }$
B) $\frac { 1 } { 4374 }$
C) $\frac { 6561 } { 2 }$
D) $\frac { 1 } { 13,122 }$

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = \frac{1}{3^8}$ and the common ratio $r = \frac{1}{3}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, where $|r| < 1$. Substituting the values, we get $S = \frac{\frac{1}{3^8}}{1 - \frac{1}{3}} = \frac{\frac{1}{3^8}}{\frac{2}{3}} = \frac{1}{2 \cdot 3^7} = \frac{1}{4374}$.

Find the Sum of the Series ∑n=8∞13n\sum _ { n = 8 } ^ { \infty } \frac { 1 } { 3 ^ { n } }n=8∑∞​3n1​

Find the Sum of the Series $\sum _ { n = 8 } ^ { \infty } \frac { 1 } { 3 ^ { n } }$