IMO 1989 LL HKG36

Origin: HKG

Problem

Prove the identity 1+ 1 2 −2 3 + 1 4 + 1 5 −2 6 +\cdot \cdot \cdot+ 1 478 + 1 479 −2 480 = 2  k=0 (161 + k)(480 −k).