Find the sum of the series, if possible.
-$$8 + 2 + \frac { 1 } { 2 } + \frac { 1 } { 8 } + \ldots$$
A) $\frac { 32 } { 3 }$
B) $\frac { 119 } { 10 }$
C) $\frac { 117 } { 10 }$
D) $\frac { 51 } { 5 }$

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = 8$ and common ratio $r = \frac{1}{4}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$ when $|r| < 1$. Substituting $a = 8$ and $r = \frac{1}{4}$, we get $S = \frac{8}{1 - \frac{1}{4}} = \frac{8}{\frac{3}{4}} = \frac{8 \cdot 4}{3} = \frac{32}{3}$.

Find the Sum of the Series, If Possible 8+2+12+18+…8 + 2 + \frac { 1 } { 2 } + \frac { 1 } { 8 } + \ldots8+2+21​+81​+…

Find the Sum of the Series, If Possible $8 + 2 + \frac { 1 } { 2 } + \frac { 1 } { 8 } + \ldots$