For positive real numbers $a_{1},a_{2},...,a_{n}$ with $a_{1}a_{2} \cdots a_{n}=1$, prove that $a_{1}^{n-1}+a_{2}^{n-1}+...+a_{n}^{n-1}\geq \frac{1}{a_{1}}+\frac{1}{a_{2}}+...+\frac{1}{a_{n}}$ .
It is from "Inequalities".
That's interesting
Last edited by *Mahi* on Sun Jul 29, 2012 8:43 pm, edited 1 time in total.
Reason: Edited: replaced "integers" with "real numbers"
Reason: Edited: replaced "integers" with "real numbers"
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Re: That's interesting
We have to use Tchebyshev's inequality here,and then AM-GM.
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sakibtanvir
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Re: That's interesting
positive integers!!!!!!!!!It would be positive quantities.Edit please.
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nafistiham
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Re: That's interesting
I suppose, that should just have been $a_{1}a_{2}...a_{n}=1$SANZEED wrote: $a_{1}a_{2},...a_{n}=1$
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Re: That's interesting
Thanks to Tiham vai.Yes that was a typo and it's edited.Thanks to Mahi vaia and Sakibtanvir too.
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