The sum of the series $1+\frac{2}{3}+\frac{4}{9}+\frac{8}{27}+\dots$ to infinity is:

Solution

1. The series is a geometric progression with $a=1$ and $r=2/3$.
2. The sum of an infinite geometric series is $S=\frac{a}{1-r}$.
3. $$\begin{array}{rl}S& =\frac{1}{1-2/3}\\ & =\frac{1}{1/3}\\ & =3\end{array}$$.
4. Hence the answer is (B).