\(C=\dfrac{2}{3\cdot5}+\dfrac{3}{5\cdot8}+\dfrac{11}{8\cdot19}+\dfrac{13}{19\cdot32}+\dfrac{25}{32\cdot57}+\dfrac{30}{57\cdot87}\)\(C=\left(\dfrac{5-3}{3\cdot5}\right)+\left(\dfrac{8-5}{5\cdot8}\right)+\left(\dfrac{19-8}{8\cdot19}\right)+\left(\dfrac{32-19}{19\cdot32}\right)+\left(\dfrac{57-32}{32\cdot57}\right)+\left(\dfrac{87-57}{57\cdot87}\right)\)\(C=\left(\dfrac{1}{3}-\dfrac{1}{5}\right)+\left(\dfrac{1}{5}-\dfrac{1}{8}\right)+\left(\dfrac{1}{8}-\dfrac{1}{19}\right)+\left(\dfrac{1}{19}-\dfrac{1}{32}\right)+\left(\dfrac{1}{32}-\dfrac{1}{57}\right)+\left(\dfrac{1}{57}+\dfrac{1}{87}\right)\)\(C=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{32}+\dfrac{1}{32}-\dfrac{1}{57}+\dfrac{1}{57}-\dfrac{1}{87}\)\(C=\dfrac{1}{3}-\dfrac{1}{87}=\dfrac{28}{87}\)