Let and let for . Prove

*Proof.*First,

for all . We then apply the Cauchy-Schwarz inequality to the numbers and . So, Cauchy-Schwarz gives us,

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Stumbling Robot

A Fraction of a Dot
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Prove the product of sums of n numbers and their reciprocals is greater than n^2

* Proof. * First,
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### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

Let and let for . Prove

for all . We then apply the Cauchy-Schwarz inequality to the numbers and . So, Cauchy-Schwarz gives us,

You can also prove it this way:

If and are the arithemetic and geometric means of the sequence , then