It must be , otherwise
Now, do you know the Means Inequalities?:
Well, taking the two extremes in the above inequalities gives you what you want. About the proof of the inequalities (well, THE inequality, since only the left one is needed: the right one follows from this taking the inverse of the elements) you can search inside MHF and look for a solution. I sent one just yesterday, in another thread)
It's here: http://www.mathhelpforum.com/math-he...-exercise.html
The second post there is mine and where I prove the inequality.