Answer:
D
Step-by-step explanation:
The sum to infinity of a geometric sequence is calculated as
[tex]S_{infinity}[/tex] = [tex]\frac{a}{1-r}[/tex] | r | < 1
where a is the first term and r the common ratio
Here a = 1 and r = [tex]\frac{1}{5}[/tex] , thus
[tex]S_{infinity}[/tex] = [tex]\frac{1}{1-\frac{1}{5} }[/tex] = [tex]\frac{1}{\frac{4}{5} }[/tex] = [tex]\frac{5}{4}[/tex] → D
