What is the sum of the infinite series 12+16+118+154+⋯+12⋅3n−1+⋯\displaystyle \frac{1}{2} + \frac{1}{6} + \frac{1}{18} + \frac{1}{54} + \cdots + \frac{1}{2 \cdot 3^{n-1}} + \cdots21+61+181+541+⋯+2⋅3n−11+⋯?
34\displaystyle \frac{3}{4}43
1\displaystyle 11
12\displaystyle \frac{1}{2}21
23\displaystyle \frac{2}{3}32
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