Respuesta :
Answer:
Option B.
Step-by-step explanation:
Consider the given geometric series is
[tex]S=20-5+\dfrac{5}{4}-\dfrac{5}{16}+...[/tex]
We need to find the sum of given series.
Here, first term is a=20 and common ratio is
[tex]r=\dfrac{-5}{20}=-\dfrac{1}{4}[/tex]
The sum of infinite GP is
[tex]S=\dfrac{a}{1-r}[/tex]
Substitute [tex]a=20\text{ and }r=\dfrac{-5}{20}=-\dfrac{1}{4}[/tex].
[tex]S=\dfrac{20}{1-(-\dfrac{1}{4})}[/tex]
[tex]S=\dfrac{20}{\dfrac{5}{4}}[/tex]
[tex]S=\dfrac{20\times 4}{5}[/tex]
[tex]S=16[/tex]
Therefore, the correct option is B.
