Solution : 

1. The collection , . ,  and  satisfies the inequality (*).
2. On the contrary, suppose that for each , . Below, the last inequality for i will be denoted by I(i). Now, I(2) , I(3) imply that  or . By the same way, I(5) , I(6) imply that . Therefore, . The sum of I(3) and I(5) gives . Taking into account I(4) we get  or . Contradiction with the above obtained .