Answer:
[tex]S(\infty)=\frac{40}{3}[/tex]
Step-by-step explanation:
we are given series as
S(infinity)=20-10+5-..
Firstly, we will check type of series
first term=20
second term=-10
third term =5
now, we can find common ratios
[tex]r=\frac{-10}{20} =-0.5[/tex]
[tex]r=\frac{5}{-10} =-0.5[/tex]
we can see that both ratios are equal
so, this is geometric series
we can use sum of infinite terms formula
[tex]S(\infty)=\frac{a}{1-r}[/tex]
where a is first term
a=20
r=-0.5
now, we can plug values
[tex]S(\infty)=\frac{20}{1+0.5}[/tex]
[tex]S(\infty)=\frac{40}{3}[/tex]
