\(\dfrac{1}{3\cdot10}+\dfrac{1}{10\cdot17}+\dfrac{1}{17\cdot24}+...+\dfrac{1}{73\cdot80}-\dfrac{1}{2\cdot9}-\dfrac{1}{16\cdot23}-\dfrac{1}{23\cdot30}\\ =\dfrac{1}{7}\left(\dfrac{7}{3\cdot10}+\dfrac{7}{10\cdot17}+\dfrac{7}{17\cdot24}+...+\dfrac{7}{73\cdot80}\right)-\dfrac{1}{7}\left(\dfrac{1}{2}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{30}\right)\\ =\dfrac{1}{7}\left(\dfrac{1}{3}-\dfrac{1}{30}\right)-\dfrac{1}{7}\left(\dfrac{1}{2}-\dfrac{1}{30}\right)=\dfrac{-1}{48}\)
\(\dfrac{1}{3.10}+\dfrac{1}{10.17}+\dfrac{1}{17.24}+...+\dfrac{1}{73.80}-\dfrac{1}{2.9}-\dfrac{1}{9.16}-\dfrac{1}{16.23}-\dfrac{1}{23.30}\\ =\dfrac{1}{3}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{24}+...+\dfrac{1}{73}-\dfrac{1}{80}-\left(\dfrac{1}{2.9}+\dfrac{1}{9.16}+\dfrac{1}{16.23}+\dfrac{1}{23.30}\right)\\ =\dfrac{1}{3}-\dfrac{1}{80}-\left(\dfrac{1}{2}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{30}\right)\\ =\dfrac{77}{240}-\left(\dfrac{1}{2}-\dfrac{1}{30}\right)\\ =\dfrac{77}{240}-\dfrac{7}{15}\\ =\dfrac{-7}{48}\)
