Q3 Matemática  (Hungary-Israel Binational 1990)

Prove que: $$\frac{1989}{2}-\frac{1988}{3}+\frac{1987}{4}-\cdots -\frac{2}{1989}+\frac{1}{1990}=\frac{1}{996}+\frac{3}{997}+\frac{5}{998}+\cdots +\frac{1989}{1990}$$