Answer:
[tex]S_\infty=250[/tex].
Step-by-step explanation:
The given infinite series is [tex]50+40+32+\frac{128}{5}+...[/tex].
The first term of this series is [tex]a_1=50[/tex].
The common ratio is [tex]r=\frac{40}{50}[/tex].
[tex]\Rightarrow r=\frac{4}{5}[/tex].
The sum of this infinite series is given by the formula,
[tex]S_\infty=\frac{a_1}{1-r}[/tex]
We now substitute all the above values in to this formula obtain,
[tex]S_\infty=\frac{50}{1-\frac{4}{5}}[/tex]
This implies that,
[tex]S_\infty=\frac{50}{\frac{1}{5}}[/tex]
This simplifies to,
[tex]S_\infty=50\times 5[/tex]
[tex]S_\infty=250[/tex].
The correct answer is C.
