Problem A. 478. (March 2009)
A. 478. If a1,a2,...,an are positive numbers with a1+a2+...+an=1, prove .
Deadline expired on 15 April 2009.
Apply Hölder's innequality on the sequences (ai1/3) and (aiai+1)1/3 (i=1,2,...,n-1), with the expononts p=3 and q=3/2:
From the estimates and
Based on the solution of Nagy János