Q34 Matemática  (IMO Longlists 1989)

Prove a identidade $$1+\frac{1}{2}-\frac{2}{3}+\frac{1}{4}+\frac{1}{5}-\frac{2}{6}+\dots +\frac{1}{478}+\frac{1}{479}-\frac{2}{480}=2\cdot \sum _{k=0}^{159}\frac{641}{(161+k)\cdot (480-k)}.$$