$ \begin{aligned}原式&=1-(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}) \\ &=1-(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+···+\frac{1}{11}-\frac{1}{12}) \\ &=1- (\frac{1}{4}-\frac{1}{12}) \\ &=1-\frac{1}{6} \\ &=\frac{5}{6} \\ \end{aligned}$
