Answer:
3rd option
Step-by-step explanation:
The sum to infinity of a geometric sequence is
S = [tex]\frac{a}{1-r}[/tex]
where a is the first term and r the common ratio
The expression inside the summation is
6 [tex](\frac{1}{3}) ^{n-1}[/tex]
which is in the form of the nth term of a geometric sequence
with a = 6 and r = [tex]\frac{1}{3}[/tex] , then
S = [tex]\frac{6}{1-\frac{1}{3} }[/tex] ← expression required
= [tex]\frac{6}{\frac{2}{3} }[/tex]
= 9
