$\dfrac{-1}{20} + \dfrac{-1}{30} +\dfrac{-1}{42} + \dfrac{-1}{56} +\dfrac{-1}{72}+ \dfrac{-1}{90}$
$= \dfrac{-1}{20} - \dfrac{1}{30} - \dfrac{1}{42} - \dfrac{1}{56} - \dfrac{1}{72} - \dfrac{1}{90}$
$= - ( \dfrac{1}{20} + \dfrac{1}{30} + \dfrac{1}{42}+ \dfrac{1}{56} +\dfrac{1}{72} + \dfrac{1}{90})$
$= - (\dfrac{1}{4.5} + \dfrac{1}{5.6} + \dfrac{1}{6.7} + \dfrac{1}{7.8} + \dfrac{1}{8.9} + \dfrac{1}{9.10})$
$= - ( \dfrac{1}{4} - \dfrac{1}{5} + \dfrac{1}{5} -\dfrac{1}{6} + \dfrac{1}{6} - \dfrac{1}{7} + \dfrac{1}{7} - \dfrac{1}{8} + \dfrac{1}{8} - \dfrac{1}{9} + \dfrac{1}{9} - \dfrac{1}{10})$
$= -(\dfrac{1}{4} - \dfrac{1}{10})$
$= - \dfrac{3}{20}$
