Answer:
b. [tex]\frac{40}{3}[/tex]
Step-by-step explanation:
The given geometric series is;
[tex]20-10+5-\frac{5}{2}+...[/tex]
The first term of this series is
[tex]a_1=20[/tex]
The common ratio is
[tex]r=\frac{-10}{20}=-\frac{1}{2}[/tex]
The sum to infinity of this series is
[tex]S_{\infty}=\frac{a_1}{1-r}[/tex]
Substitute the given values to obtain;
[tex]S_{\infty}=\frac{20}{1--\frac{1}{2}}[/tex]
This implies that;
[tex]S_{\infty}=\frac{20}{\frac{3}{2}}[/tex]
[tex]S_{\infty}=\frac{40}{3}[/tex]
