olymmath

ISL 1989 Problem 34

    Prove the identity

    1+12−23+14+15−26+…+1478+1479−2480=2⋅∑k=0159641(161+k)⋅(480−k).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} = 2 \cdot \sum^{159}_{k=0} \frac{641}{(161+k) \cdot (480-k)}.

    Dataset text AI-MO AoPS. Quoted with source.

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