A geometric series is characterized by a common ratio.
The sum of the infinite geometric series is -288
The geometric series is given as:
[tex]\mathbf{\sum\limits^{\infty}_{n = 1}(-144)(\frac{1}{2})^{n-1})}[/tex]
From the geometric series, we have the following parameters
[tex]\mathbf{a = -144}[/tex] --- the first term
[tex]\mathbf{r = \frac 12}[/tex] --- the common ratio
The sum to infinity of a geometric series is calculated using the following formula
[tex]\mathbf{S_{\infty} = \frac{a}{1 - r}}[/tex]
Substitute values for the first term (a) and the common ratio (r)
[tex]\mathbf{S_{\infty} = \frac{-144}{1 - 1/2}}[/tex]
Simplify the denominator
[tex]\mathbf{S_{\infty} = \frac{-144}{1/2}}[/tex]
Divide
[tex]\mathbf{S_{\infty} = -288}[/tex]
Hence, the sum of the infinite geometric series is -288
Read more about infinite geometric series at:
https://brainly.com/question/4268280
