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!)
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
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?
This is a classical technique, but it’s also not surprising that it would work. If you want the arithmetic mean to remain the same you’d need to keep the rest of the terms the same as the AM.
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!)
Good idea. Yes, that’s an important inequality.
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
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.
That’s a good approach
ruclips.net/video/fddgKeguVl4/видео.html
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?
This is a classical technique, but it’s also not surprising that it would work. If you want the arithmetic mean to remain the same you’d need to keep the rest of the terms the same as the AM.