IMO 1979 LL BRA9
The real numbers lpha1, lpha2, lpha3, . . . , lphan are positive. Let us denote
IMO 1979 LL BRA9
Origin: BRA
Problem
The real numbers \alpha1, \alpha2, \alpha3, . . . , \alphan are positive. Let us denote by h = n 1/\alpha1+1/\alpha2+\cdot\cdot\cdot+1/\alphan the harmonic mean, g = n\sqrt\alpha1\alpha2 \cdot \cdot \cdot \alphan the geometric mean, a = \alpha1+\alpha2+\cdot\cdot\cdot+\alphan n the arithmetic mean. Prove that h \leq g \leqa, and that each of the equalities implies the other one.