пешечка

(no subject)

Let a1,a2,...,an be a positive real numbers. Let A =(a1+a2+...+an)/n, G=(a1xa2x...xan)^(1/n), H=n/( (1/a1)+(1/a2)+...+(1/an) ).
It is well-known that A=>G=>H. Proof more strong un-equalities: A^(n-1)xH => G^n. There is very short proof!