AM-GM Inequality | Arithmetic Mean Geometric Mean Inequality

Показать описание

In this video we give a proof of the AM-GM Inequality, that is the arithmetic mean geometric mean inequality. Our proof follows that outlined in Cambridge Part 3 2018 problem 5. It is a nice application of calculus and inequalities to establish the AM-GM inequality.

#ArithmeticMeanGeometricMeanInequality #AMGMInequality #Inequalities

CHECK OUT OTHER TYPES OF VIDEOS:
================================

GET MY BOOK ON AMAZON!!
========================

"Number Theory Towards RSA Cryptography in 10 Undergraduate Lectures"

CHECK ME OUT ON THE INTERNET!!
==============================

TikTok: @profomarmath
Twitter: @ProfOmarMath
Instagram: profomarmath

And of course, subscribe to my channel!

Рекомендации по теме

Комментарии

In the final arguments a_3=G_2 so a_3^2=a_1a_2 and hence a_3=a_1=a_2

ProfOmarMath

I have studied am gm but not seen proof but now i understand nyc vedio

deepjyoti

And what about exp(ln .... + ln an)/n)? ln is concave function.

tgx

Sir nice video again, also is there a way to prove GM HM inequality

akshataggarwal

i expect that at the time 10 march 2022 you will have more than 25000 subscribers!

aashsyed

At 11:42, I am not sure I follow the calculation. You have:
(a3/G2)^(1/3) = 1
(a3/G2) = 1
...
a3 = cuberoot(a1a2a3) = G3.
I am not sure how the G2 became G3 here.
The computation still makes sense because it is clear that a_i=a_j (i != j) for all distinct i and j if and only if An = Gn = a1, for all n, so the values for An and Gn remain constant as n changes. However, since this is what you are trying to prove here, this doesn't quite hold. I think that the computation is supposed to be that:

(a3/G2)^(1/3) = 1
(a3/G2) = 1
a3 = G2 = sqrt(a1a2)
a3^2 = a1a2 = a1^2
a3 = a1, and similar for other \lambda_k values.

That said, love the video and your content!

bencheesecake

Can you please make a video on how to convert absolute value functions to piecewise functions? Take some complex examples like involving e^x, etc please.

VishnuSrivatsava

At the end you make a small error, you keep evealuating G_n at G_n+1, however the correct evaluation yields same result luckily

tomatrix

Hi ProfOmar. Nice proof of the AM-GM inequality, thanks for posting, but might be a little difficult for some people to follow. I have an alternative proof which I believe is a bit easier to follow. If you're interested to see this, let me know. Alex Z, Maths Tutor.

azmath

i am going to to prove am-gm inequality when n=2

aashsyed

AM-GM Inequality | Arithmetic Mean Geometric Mean Inequality

AM-GM Inequality | Arithmetic Mean Geometric Mean Inequality

AM-GM Inequality VI (visual proof)

AM-GM Inequality II

AM-GM Inequality II (visual proof)

Visual Proof of AM-GM Inequality I

Problem-Solving Trick No One Taught You: RMS-AM-GM-HM Inequality

AM-GM Inequality via negative space

AM-GM inequality visually

Patterns To Solve Any Math Questions || JEE & BITSAT Entrance Exams

Prove the Inequality of Arithmetic and Geometric Means (AM-GM inequality)

[AM-GM Inequality for n terms] Forwards Backwards Induction - Proof of AM-GM Inequality for n terms

Fold the AM-GM inequality

Inequalities Tutorial #1 - Intro to AM-GM

AM-GM Inequality IV (visual proof)

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

AM/GM Inequality (1 of 2: Geometric Proof)

Proof: Arithmetic Mean is Greater Than Geometric Mean

A Question Based on AM GM Inequality

AM-GM inequality: proof & application (Exam Question 11 of 12)

Unleash the Power of Induction: Proving AM/GM Inequality with Two Ingenious Algebra Tricks

Arithmetic Mean - Geometric Mean Inequality (AM-GM)

Arithmetic geometric mean inequality

Proof of the AM-GM Inequality

Arithmetic Mean AM vs Geometric Mean GM Visual Proof