IMO 1974 LL FIN14

Let n and k be natural numbers and a1, a2, . . . , an positive real

imolonglistmathematicsolympiad

IMO 1974 LL FIN14

Origin: FIN

Problem

Let n and k be natural numbers and a1, a2, . . . , an positive real numbers satisfying a1 + a2 + \cdot \cdot \cdot + an = 1. Prove that a−k

  • a−k
  • \cdot \cdot \cdot + a−k n \geqnk+1.