sum(k=1, infty) \dfrac{3}{2}\cdot (\dfrac{2}{9})^k \cdot \dfrac{(2k-2)!}{k(k-1)!^2}sum(k=1, infty) \dfrac{3}{2}\cdot (\dfrac{2}{9})^k \cdot \dfrac{(2k-2)!}{k(k-1)!^2}

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