Answer:
D: 32/5
Step-by-step explanation:
Given series is 8 -2 + 1/2 - 1/8+.....
to find the sum we use formula
[tex]S_n = \frac{a}{1-r}[/tex]
where a is the first term
r is the common ratio
To find common ratio we divide second term by first term
[tex]r= \frac{-2}{8} =\frac{-1}{4}[/tex]
a= 8
Now plug inthe values and find out the sum
[tex]S_n = \frac{a}{1-r}[/tex]
[tex]S_n = \frac{8}{1-\frac{-1}{4}}[/tex]
[tex]S_n = \frac{8}{1+\frac{1}{4}}[/tex]
[tex]S_n = \frac{8}{\frac{5}{4}}[/tex]
[tex]S_n = 8*\frac{4}{5}[/tex]
sum = 32/ 5
