不等式

$$ \begin{aligned} H{n}&=\frac{n}{\sum_{i=1}^{n}\frac{1}{x{i}}} = \frac{n}{\frac{1}{x{1}}+ \frac{1}{x{2}}+ \cdots + \frac{1}{x{n}}} \\ G{n} &=\sqrt[n]{\prod _{i=1}^{n}x{i}}= \sqrt[n]{x{1}x{2}\cdots x{n}} \\ A{n}&=\frac{1}{n}\sum _{i=1}^{n}x{i}=\frac{x{1}+ x{2}+ \cdots + x{n}}{n} \\ Q{n} &=\sqrt{\sum _{i=1}^{n}x{i}^{2}} =\sqrt{\frac{x{1}^{2}+ x{2}^{2}+ \cdots + x{n}^{2}}{n}} \end{aligned} $$

$$H{n}\leq G{n}\leq A{n}\leq Q{n}$$