$$ \frac{1}{n} \sum_{i=1}^n x_i \geq \left(\prod_{i=1}^n x_i\right)^{\frac{1}{n}} $$ I need to prove this inequality for positive numbers $x_1$,...,$x_n$ using investigation of extremum, but I even don`t know from what to start, pls help.
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do you mean $$\frac{1}{n}\sum_{i=1}^n x_i\geq \sqrt[n]{\prod_{i=1}^n x_i}$$ – Dr. Sonnhard Graubner Nov 06 '17 at 21:29
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Yes,you are right,sorry – PashaMinigun Nov 06 '17 at 21:35
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see here https://math.stackexchange.com/questions/691807/proofs-of-am-gm-inequality – Dr. Sonnhard Graubner Nov 06 '17 at 21:39
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This is the classical AM/GM inequality. – Angina Seng Nov 06 '17 at 21:45
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Dr. Sonnhard Graubner, thank you! – PashaMinigun Nov 06 '17 at 21:46