Prove the second inequality assuming the first

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Homework Help Overview

The discussion revolves around proving the second inequality given the first, as outlined in a linked document. The subject area pertains to inequalities in mathematics.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss hints provided and explore the applicability of the first inequality to the expression presented. There are attempts to manipulate the inequalities using various mathematical techniques, including logarithms and common denominators.

Discussion Status

The discussion is ongoing, with participants expressing uncertainty about their manipulations and seeking clarification on the approach. Some guidance has been offered regarding the form of the expression in relation to the first inequality.

Contextual Notes

Participants indicate a struggle with the manipulation of the inequalities and express concerns about missing obvious steps. There is a sense of frustration regarding the complexity of the problem.

ehrenfest
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Homework Statement



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

Can someone give me a hint on problem 1?

Homework Equations





The Attempt at a Solution

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




















Isn't the expression

[tex]\left( \frac{ \frac{1}{a_1} + \cdots + \frac{1}{a_n} }{n} \right)^{-1}[/tex]

already in a form to which the first inequality is applicable?
 
Last edited:
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...
 
Bah, you saw it before I edited my post. :-p
 
Wow. I feel stupid now. :)
 

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