Use the Formula for the Sum of an Infinite Geometric Series
-$$2 + \frac { 2 } { 3 } + \frac { 2 } { 9 } + \frac { 2 } { 27 } + \ldots$$
A) 3
B) $\frac { 8 } { 3 }$
C) $\frac { 2 } { 3 }$
D) does not exist

Question

Quizplus · Accepted Answer

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

Use the Formula for the Sum of an Infinite Geometric 2+23+29+227+…2 + \frac { 2 } { 3 } + \frac { 2 } { 9 } + \frac { 2 } { 27 } + \ldots2+32​+92​+272​+…

Use the Formula for the Sum of an Infinite Geometric $2 + \frac { 2 } { 3 } + \frac { 2 } { 9 } + \frac { 2 } { 27 } + \ldots$