Proving the Arithmetic Geometric Mean inequality (Am

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Proving the Arithmetic Geometric Mean inequality (Am - Gm proof) with induction

Рет қаралды 7,778

Shefs of Problem Solving

Күн бұрын

This proof uses only elementary properties of algebra and a cool induction idea

Пікірлер: 18

@tigeronion Ай бұрын

The famous Cauchy proof. Nice!

@Jancel705 15 сағат бұрын

great proof, i think you forgot to set X to min({a}_{n+1}^{2^\alpha}) to ensure boundedness tho

@MyOneFiftiethOfADollar Жыл бұрын

Liked the how you "filled in the gaps" between powers of 2 informally, before you got to the formality of the induction proof.

@williampluim844 Ай бұрын

You're a beast. Thanks!

@samkerr1826 7 ай бұрын

This guy is the Hans Neimann of Maths

@dddddd-jj5md 2 ай бұрын

lol

@user-tv3lc6eu2y 2 жыл бұрын

My favorite proof uses Jensen's inequality (applying to concavity of ln x)

@ShefsofProblemSolving 2 жыл бұрын

Oh that's actually pretty cool

@ahmedlutfi4894 8 ай бұрын

wow the explanation is making alot of sense there is no blank spaces while following up

@kenchen9198 2 ай бұрын

thanks，this video helps me a lot❤

@thealgebraicadventures-bz6pz 3 ай бұрын

13:00 nice technique 😃

@user-qi4fq3gz6d 6 ай бұрын

can you help?...when should we use iff symbol in our maths equation or proof etc

@thedeathofbirth0763 Жыл бұрын

Can you make another video and explain the general case a bit more in detail please. I could follow your reasoning till the general case. I really want to understand this. Thank you. Why the last term wasn't raised to (1/2^a) for instant?! Why you took n< 2^a in the first place, because to me it won't make it the general case but for the number of elements to be powers of two!

@ShefsofProblemSolving Жыл бұрын

We showed AmGm for all powers of two. Now the general case is that we take an n that's not a power of 2 and let is be less than some power of two. Now we take the thing we knew for powers of two that holds true and show that if we plug in a couple of identical values we'll get the inequality for n. That's the idea

@thedeathofbirth0763 Жыл бұрын

@@ShefsofProblemSolving I see, thank you for the time you took to explain it more clearly.