The Harmonic Mean and the AM-HM Inequality
Read this topicExplanations 3
- Inequalities (Part 3) In this part, we'll look at more advanced applications of AM-GM. First, we show the AM-GM-HM inequality, which is a1+a2+...+ann≥a1a2...ann≥n1a1+1a2+...+1an…
By Zi Song Yeoh
- The arithmetic mean and harmonic mean of a set of nnn positive integers x1,x2,…,xnx_1, x_2, \dots , x_nx1,x2,…,xn are respectively given by x1+x2+⋯+xnn\frac{x_1+x_2 + \cdots …
By Rithvik Pasumarty
- Here's a proof of AM-HM using just AM-GM. 1a1+⋯+1ann≥1a1…1ann\frac{\frac1{a_1}+\dots+\frac1{a_n}}n\ge\sqrt[n]{\frac1{a_1}\dots\frac1{a_n}}na11+⋯+an1≥na11…an1 n1a1+⋯+1a…
By Cody Johnson