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Montrer que : \[\forall n\in \Nn^{*},\forall (x_{1},...,x_{n})\in \left( {\Rr}^{+*}\right)^{n}, 1+\left( \prod\limits_{k=1}^{n}x_{k}\right) ^{\frac{1}{n}}\leq \left( 1+\prod\limits_{k=1}^{n}x_{k}\right) ^{\frac{1}{n}}.\]
Montrer que : \[\forall n\in \Nn^{*},\forall (x_{1},...,x_{n})\in \left( {\Rr}^{+*}\right)^{n}, 1+\left( \prod\limits_{k=1}^{n}x_{k}\right) ^{\frac{1}{n}}\leq \left( 1+\prod\limits_{k=1}^{n}x_{k}\right) ^{\frac{1}{n}}.\]