在不等式的证明中,经常要用到一些重要不等式,平均值不等式就是其中一个.设a1,a2,…,an∈R*,将An=a1+a2+…+ann,Gn=na1a2…an,Hn=n1a1+1a2+…+1an,Qn=a12+a22+…+an2n分别叫做这n个正数的算术平均数、几何平均数、调和平均数和平方平均数,则有下面的平均值不等式成立.定理Hn≤G In the proof of inequality, it is often necessary to use some important inequalities, the mean inequality is one of them. Let a1, a2, ..., an∈R * set An = a1 + a2 + ... + ann, Gn = na1a2 ... an, Hn = n1a1 + 1a2 + ... + 1an, Qn = a12 + a22 + ... + an2n are called arithmetic mean, geometric mean, harmonic mean and square mean of the n positive numbers, respectively, and the following inequalities of the mean hold. Hn≤G