Respuesta :
Answer:
A
Step-by-step explanation:
The sum to infinity of a geometric series is
S (∞ ) = [tex]\frac{a}{1-r}[/tex] ( - 1 < r < 1 )
where a is the first term 8 and r is the common ratio, hence
S(∞ ) = [tex]\frac{8}{1-\frac{1}{2} }[/tex] = [tex]\frac{8}{\frac{1}{2} }[/tex] = 16
This sum of the infinite geometric series is 16 since the correct option is (A) 16.
Definition of infinite geometric series:
The sum of infinite geometric sequences is called an infinite geometric series. There would be no final term in this series. The infinite geometric series has the general form a1+a1r+a1r2+a1r3+..., where a1 is the first term and r is the common ratio. The sum of all finite geometric series can be found.
How to find the sum of the series?
In terms of the first term a1 and the common ratio r, the sum is...[tex]S =\frac {a_1}{(1-r)}[/tex]
We discover... by substituting the given numbers and performing the arithmetic...[tex]S = 8/(1 -1/2) = 16[/tex]
The total number of items in the series is 16.
Learn more about infinite geometric series here, https://brainly.com/question/27350852
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