Find the sum of the infinite series

MATHEMATICS · Single correct · AoPS · Mathematics · Sequences & Series · Sequences & Series

Problem

\frac{1}{9} + \frac{1}{18} + \frac{1}{30} + \frac{1}{45} + \frac{1}{63} + \dots

(a)

\frac{1}{3}

(b)

\frac{1}{4}

(c)

\frac{1}{5}

(d)

\frac{2}{3}