Proof of the AM-GM Inequality

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In this video I present a proof of the Arithmetic Mean-Geometric Mean Inequality.
  1. Dr. Ebrahimian
  2. Math
  3. Maths
  4. Math Competitions
  5. Math Competition
  6. AM-GM Inequality
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Комментарии
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Maybe you can also do a video / proof about power means inequality. I don't know how often that comes up for competitions but it's a nice generalization (and easy to remember!)

Quantris
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i have two pieces of advice:
(1) don't skip too many steps; some steps are not as obvious for typical people and you should keep them in your demonstration
(2) explain briefly the logic/thinking of this Cauchy Induction

patrick
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i dont know if u know about the Jensen Inequality but if we use that on the curve ln(x) then we can very easily prove AM-GM inequality.

cyanide
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why can we set x_(n+1)=...=x_m all equal to A?
ahhhh nvm i gotya 👍
how did u come up with this proof and know that setting x_1=...=x_n to A and all the others to A was gonna cancel out etc. and leave you with the result you wanted? just practice?

hjker