高中生都能看懂的11种算数不等式证明 (11 proof of Inequality of arithmetic and geometric means) transcendent 爱子是那不能看见之神的像,是首生的,在一切被造的以先。2 人赞同了该文章 作者懒,不定期填坑 自从算数不等式被发现以来已经有了114514种论证(迫真), 以下我会以高中生都能理解的方式为各位介绍...
Arithmetic Series of First/k-th Order: Geometric Series: Special Finite Series: Arithmetic Mean or Arithmetic Average: Geometric Mean or Geometric Average: Harmonic Mean: Quadratic Mean: Relations Between the Means of Two Positive Values: 3 不等式 3.1 Pure Inequalities Inequalities: Solution of Inequ...
WegetCombinatoralInequality ( 1 )Gn+1 ≤ {P∫∞ 0 [∏n k=0 (x+ n k ) qk]-p- 1dx}- 1 /p ≤An+1 ; ( 2 )e≤ lim n→∞{P∫∞ 0 [∏n k=0 (x+ n k ) ]- (p+1 ) /n+1dx}- 1 /p ≤ 2 ; ( 3)Gn+1 ≤J(a ,q,p) ≤J(a,q,p ,l,λ)≤An+1 Here,J...
infimum: 等; inequality of arithmetic and geometric means: 平均数不等式; infimum: 下确界; ... www.docin.com|基于19个网页 2. 算术几何平均不等式 1. 使用归纳法, 注意 \((1)\), 可以容易的证明算术几何平均不等式(Inequality of arithmetic and geometric means).2. (04 年国家队...www.zyymat....
首先，算数不等式陈述了当[公式]且X非负时，以下关系成立：[公式]或者更具体地，[公式]时等式成立，即[公式]。那么，这个不等式究竟有何作用呢？它在实际问题中可以简化求解，例如，当a和b为正实数时，我们可以通过不等式求解[公式]。下面以一个实例说明，通过不等式构造，我们发现[公式]，将这个不...
Then the following inequalities hold:n1a 1+ ··· +1a n≤n√ a1 · a 2 ··· a n≤a 1 + ··· + a nn| {z }Harmonic Mean| {z }Geometric Mean| {z }Arithmetic MeanIn all cases equality holds if and only if a 1 = ··· = a n .2. Power Means Inequality. The AM-...
arithmetic_and_geometric_sequences46ppt 系统标签: arithmeticgeometriccommondifferencesumofcommonrationth 9.2–ArithmeticSequencesandSeriesAnintroduction………1,4,7,10,139,1,7,156.2,6.6,7,7.4,3,6 ArithmeticSequencesADDTogetnextterm2,4,8,16,329,3,1,1/31,1/4,1/16,1/64,2.5,6.25 GeometricSeque...
Computation of Gauss's arithmetic-geometric mean involves iteration of a\nsimple step, whose algebro-geometric interpretation is the construction of an\nel... R Donagi,R Livne 被引量: 0发表: 1997年 Greek Means and the Arithmetic-Geometric Mean Computation of Gauss's arithmetic-geometric mean ...
dextrous manipulation planningdifferential kinematic equationIn this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.doi:10.1109/ROBOT.1998.680598Lin, HaoxiangMathematics...
The arithmetic-geometric mean agm(a,b) of two numbers a and b (often also written AGM(a,b) or M(a,b)) is defined by starting with a_0=a and b_0=b, then iterating a_(n+1) = 1/2(a_n+b_n) (1) b_(n+1) = sqrt(a_nb_n) (2) until a_n=b_n to the desired ...