Use the Formula for the Sum of an Infinite Geometric Series
-$$- 6 - 2 - \frac { 2 } { 3 } - \frac { 2 } { 9 } - \ldots$$
A) $- 9$
B) 3
C) $= \frac { 26 } { 0 }$
D) does not exist 3

Question

Quizplus · Accepted Answer

To use the formula for the sum of an infinite geometric series, we need to first check if the series is convergent. 
We can see that the common ratio between each term is $\frac{-2}{3}$. Since the absolute value of the common ratio is less than 1, the series is convergent. 
Now, we can use the formula: 
$$S=\frac{a_1}{1-r}$$ 
where $S$ is the sum of the series, $a_1$ is the first term, and $r$ is the common ratio. 
Plugging in the values from the given series, we have: 
$$S=\frac{-6}{1-\left(\frac{-2}{3}\right)}=\frac{-6}{\frac{5}{3}}=-9$$ 
Therefore, the sum of the given infinite geometric series is $-9$.

Use the Formula for the Sum of an Infinite Geometric −6−2−23−29−…- 6 - 2 - \frac { 2 } { 3 } - \frac { 2 } { 9 } - \ldots−6−2−32​−92​−…

Use the Formula for the Sum of an Infinite Geometric $- 6 - 2 - \frac { 2 } { 3 } - \frac { 2 } { 9 } - \ldots$