SOLUTION
The question simply means that we should find the sum to infinity of the geometric series.
The formula of sum to infinity of a geometric serie is given by
[tex]S_{\infty}=\frac{a}{1-r}[/tex]
Where
[tex]\begin{gathered} S_{\infty}\text{ is the sum to infinity} \\ \\ a\text{ is the first term = 1} \\ \\ r\text{ is the common ratio = }\frac{2}{3} \end{gathered}[/tex]
So, this becomes
[tex]\begin{gathered} S_{\infty}=\frac{a}{1-r} \\ \\ S_{\infty}=\frac{1}{1-\frac{2}{3}} \\ \\ S_{\infty}=\frac{1}{\frac{3-2}{3}} \\ \\ S_{\infty}=\frac{1}{\frac{1}{3}} \\ \\ S_{\infty}=3 \end{gathered}[/tex]
Therefore, option b is the correct answer
