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Does anyone know how to determine which of the following sum is larger? Thanks a lot!

[tex]

\sum_{i=1}^n a_i^{1/3}\sum_{i=1}^n a_i

[/tex]

[tex]

n\sum_{i=1}^n a_i^{4/3}

[/tex]

[tex]

a_i>0 \forall i

[/tex]

This is two polynomial of the same order. It is not clear to determine which one is larger, if I take the derivatives.

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# Inequality of exponent

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