Find the sum of the series.
-$$\sum _ { n = 0 } ^ { \infty } \frac { 8 } { 7 ^ { n } }$$
A) $\frac { 4 } { 3 }$
B) 7
C) 1
D) $\frac { 28 } { 3 }$

Question

Quizplus · Accepted Answer

We can use the formula for the sum of an infinite geometric series, which is:

$$\sum_{n=0}^{\infty}ar^n = \frac{a}{1-r}$$

where $a$ is the first term and $r$ is the common ratio.

In this case, $a=8$ and $r=\frac{1}{7}$. So the sum of the series is:

$$\sum_{n=0}^{\infty}\frac{8}{7^n} = \frac{8}{1-\frac{1}{7}} = \frac{8}{\frac{6}{7}} = \frac{56}{6} = \boxed{\frac{28}{3}}$$

Find the Sum of the Series ∑n=0∞87n\sum _ { n = 0 } ^ { \infty } \frac { 8 } { 7 ^ { n } }n=0∑∞​7n8​