The sum of the given infinite geometric series is -6.
The given geometric series is,
![-3,-\dfrac{3}{2},-\dfrac{3}{4},......](https://tex.z-dn.net/?f=-3%2C-%5Cdfrac%7B3%7D%7B2%7D%2C-%5Cdfrac%7B3%7D%7B4%7D%2C......)
It is required to find the sum of infinite geometric series.
<h3>How to find the sum of the infinite geometric series?</h3>
The formula for sum of infinite geometric series is,
![S=\dfrac{a}{1-r}](https://tex.z-dn.net/?f=S%3D%5Cdfrac%7Ba%7D%7B1-r%7D)
where a is the first term and r is the common ratio.
In the given series, the first term is -3 and the common ratio is
.
So, the sum of the series can be calculated as,
![S=\dfrac{a}{1-r}\\ S=\dfrac{-3}{\frac{1}{2}}\\ S=-3\times 2\\ S=-6](https://tex.z-dn.net/?f=S%3D%5Cdfrac%7Ba%7D%7B1-r%7D%5C%5C%0AS%3D%5Cdfrac%7B-3%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%0AS%3D-3%5Ctimes%202%5C%5C%0AS%3D-6)
Therefore, the sum of the given infinite geometric series is -6.
For more details about geometric series, refer to the link:
brainly.com/question/2501276