IMO 1989 LL MON68

If 0 < k \leq1 and ai are positive real numbers, i = 1, 2, . . . , n,

imolonglistmathematicsolympiad

IMO 1989 LL MON68

Origin: MON

Problem

If 0 < k \leq1 and ai are positive real numbers, i = 1, 2, . . . , n, prove that  a1 a2 + \cdot \cdot \cdot + an k

  • \cdot \cdot \cdot +  an a1 + \cdot \cdot \cdot + an−1 k \geq n (n −1)k .