2023年12月11日 · 定义1: 算术平均值 缩写 (AM) \frac {x_1+x_2+...+x_n} {n}\\定义2: 几何平均值 缩写 (GM) \sqrt [n] {x_1x_2...x_n}\\ 定义3: 平方平均值 缩写 (QM) \sqrt {\frac …

In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than …

AM-GM不等式：若干正数的 算术平均 值（arithmetic mean）不小于其 几何平均 值(geometric mean)， 设 a_1,a_2,\cdots,a_n>0, 则 \frac{a_1+a_2+\cdots+a_n}{n}\geq \sqrt[n]{a_1a_2\cdots …

The Mean Inequality Chain, also called the RMS-AM-GM-HM Inequality, relates the root mean square, arithmetic mean, geometric mean, and harmonic mean of a list of nonnegative reals. …

2014年2月27日 · AM-GM inequality says that for any $ a_1, \dots , a_n > 0 $, we have $ \dfrac{a_1 + \cdots + a_n}{n} \geq \sqrt[n]{a_1 \cdots a_n} $ with equality holding if and only if …

2024年7月1日 · am-gm不等式：也叫均值不等式，·即调和平均数不超过几何平均数，几何平均数不超过算术平均数，算术平均数不超过平方平均数，简记为“调几算方”。 1、下式被称为调和 …

2022年7月24日 · 对 a_1,...,a_{n-1},\frac{s}{n-1} 应用 n 元AM-GM(假设其成立)，那么就有 s+\frac{s}{n-1}=a_1+...+a_{n-1}+\frac{s}{n-1}\ge n\sqrt[n]{\frac{a_1a_2...a_{n-1}s}{n-1}}\\ …

2021年7月2日 · 其中，算术-平方平均不等式（Arithmetic Mean-Quadratic Mean Inequality），也称为AM-QM不等式，表明对于任何非负实数$x_1, x_2, ..., x_n$， 其算术... 均值 不等式 求最 …

We will look at the following 5 general ways of using AM-GM: the inequality case. The simplest way to apply AM-GM is to apply it immediately on all of the terms. For example, we know that …

Base Case: The smallest nontrivial case of AM-GM is in two variables. By the properties of perfect squares (or by the Trivial Inequality), with equality if and only if , or . Then because and are …