S = \(\dfrac{1}{1\cdot2\cdot3}+\dfrac{1}{2\cdot3\cdot4}+...+\dfrac{1}{6\cdot7\cdot8}\)
S = \(\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+...+\dfrac{1}{6\cdot7}-\dfrac{1}{7\cdot8}\)
S = \(\dfrac{1}{1\cdot2}-\dfrac{1}{7\cdot8}\)
S = \(\dfrac{1}{2}-\dfrac{1}{56}\)
S = \(\dfrac{27}{56}\)