\(=\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+\dfrac{1}{156}\)
\(=\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{12}-\dfrac{1}{13}\)
\(=\dfrac{1}{2}-\dfrac{1}{11}+\dfrac{1}{156}\)
\(=\dfrac{9}{22}+\dfrac{1}{156}=\dfrac{713}{1716}\)