APFIVE Sum of an Infinite Geometric Series
What is the sum of the infinite series $$\displaystyle \frac{1}{2} + \frac{1}{6} + \frac{1}{18} + \frac{1}{54} + \cdots + \frac{1}{2 \cdot 3^{n-1}} + \cdots$$?
A
$$\displaystyle 1$$
B
$$\displaystyle \frac{3}{4}$$
C
$$\displaystyle \frac{1}{2}$$
D
$$\displaystyle \frac{2}{3}$$
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