\(\left(-\frac{1}{2}\right)-\left(-\frac{3}{5}\right)+\left(-\frac{1}{9}\right)+\frac{1}{127}-\frac{7}{18}+\frac{4}{35}-\left(-\frac{2}{7}\right)=-\frac{1}{2}+\frac{3}{5}-\frac{1}{9}+\frac{1}{127}-\frac{7}{18}+\frac{4}{35}+\frac{2}{7}=\frac{1}{127}\)