IMO 1970 LL BEL9

Origin: BEL

Problem

If n is even, prove that 1 −1 2 + 1 3 −1 4 + \cdot \cdot \cdot −1 n = 2  n + 2 + n + 4 + n + 6 + \cdot \cdot \cdot + 1 2n  .