# Prove the second inequality assuming the first

1. Nov 8, 2007

### ehrenfest

1. The problem statement, all variables and given/known data

http://www.math.cornell.edu/~putnam/ineqs.pdf

Can someone give me a hint on problem 1?

2. Relevant equations

3. The attempt at a solution

2. Nov 9, 2007

### Hurkyl

Staff Emeritus
You were already given a hint: prove the second inequality assuming the first. Second hint below:

Isn't the expression

$$\left( \frac{ \frac{1}{a_1} + \cdots + \frac{1}{a_n} }{n} \right)^{-1}$$

already in a form to which the first inequality is applicable?

Last edited: Nov 9, 2007
3. Nov 9, 2007

### ehrenfest

Yes. I read the problem. I spent 30 minutes manipulating both the first and the second inequality. Maybe I am missing something obvious, but I just don't see how to manipulate correctly. I tried logarithms, finding common denominators...

4. Nov 9, 2007

### Hurkyl

Staff Emeritus
Bah, you saw it before I edited my post. :tongue:

5. Nov 9, 2007

### ehrenfest

Wow. I feel stupid now. :)