${\frac{-1}{2}+\frac{3}{5}+\frac{-1}{9}+\frac{1}{127}+\frac{-7}{8}+\frac{4}{35}+\frac{2}{7}}$
= ${ (\frac{-1}{2}+\frac{-7}{8})+(\frac{3}{5}+\frac{4}{35}+\frac{2}{7})+ (\frac{-1}{9}+\frac{1}{127})}$
= ${(\frac{-4}{8}+\frac{-7}{8})+(\frac{21}{35}+\frac{4}{35}+\frac{10}{35})+(\frac{-127}{1143}+\frac{9}{1143})}$
= ${ \frac{-11}{8}+ 1+ \frac{-118}{1143}}$
= ${\frac{-12573}{9144}+\frac{9144}{9144}+\frac{-944}{9144}}$
= ${ \frac{-4373}{9144}}$
