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设ａ１，ａ２，…，ａｎ＞０，对每个ｋ（１≤ｋ≤ｎ），记Ａｋ＝１ｋ（ａ１＋ａ２＋…＋ａｋ） Ｇｋ＝ｋａ１ａ２…ａｋ，则Ａｋ≥Ｇｋ，ｋ＝１，２，…，ｎ．且有Ｆ．Ｈｏｌｌａｎｄ提出的混合平均不等式 ｎＡ１Ａ２…Ａｎ≥１ｎ（Ｇ１＋Ｇ２＋…＋Ｇｎ）①仅当ａ１＝ａ２?
Let a1,a2,...,an>0, for each k (1≤k≤n), remember that Ak=1k(a1+a2+...+ak) Gk=ka1a2...ak, then Ak≥Gk,k=1,2,... , n. And there is F. Holland’s mixed average inequality nA1A2...An≥1n(G1+G2+...+Gn)1 only if a1=a2?