Pruebe la identidad \[ 1 + \frac{1}{2} - \frac{2}{3} + \frac{1}{4} + \frac{1}{5} - \frac{2}{6} + \ldots + \frac{1}{478} + \frac{1}{479} - \frac{2}{480} \n= 2 \cdot \sum^{159}_{k=0} \frac{641}{(161+k) \cdot (480-k)}.\]