if :
Prove that :
Shouldn't it be: too?
We have:
- all the sums are cyclic-
Thus: iff (1)
Now: (2)
Let , then (2) is equivalent to: -remember, it's cyclic-
By Cauchy-Schwarz: (3)
Let then :
Thus by (3) we have:
But since by AM-GM inequality -remember -, it follows that which proves (1)
Since and