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

Question

Quizplus · Accepted Answer

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

Find the Sum of the Series ∑n=0∞(−1)n87n\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { 8 } { 7 ^ { n } }n=0∑∞​(−1)n7n8​

Find the Sum of the Series $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { 8 } { 7 ^ { n } }$