Answer:
[tex]Sum=\frac{32}{5}=6.4[/tex]
Step-by-step explanation:
we are given geometric series as
[tex]8-2+\frac{1}{2}-\frac{1}{8}+.......[/tex]
we can use infinite sum formula
[tex]sum=\frac{a}{1-r}[/tex]
where
a is first term
r is common ratio
so, we have
[tex]a=8[/tex]
[tex]r=\frac{-2}{8}[/tex]
[tex]r=-\frac{1}{4}[/tex]
now, we can plug values
[tex]sum=\frac{8}{1-(-\frac{1}{4})}[/tex]
[tex]Sum=\frac{32}{5}=6.4[/tex]
