math-test

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$\left(a\pm b\right)^2=a^2\pm2ab+b^2$

$x ={-b \pm \sqrt{b^2-4ac}\over 2a}$

$ H_{n}=\frac{n}{\sum \limits_{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 \limits_{i=1}^{n}x_{i}}= \sqrt[n]{x_{1}x_{2}\cdots x_{n}} $

$A_{n}=\frac{1}{n}\sum \limits_{i=1}^{n}x_{i}=\frac{x_{1}+ x_{2}+ \cdots + x_{n}}{n} $

$ Q_{n}=\sqrt{\sum \limits_{i=1}^{n}x_{i}^{2}}= \sqrt{\frac{x_{1}^{2}+ x_{2}^{2}+ \cdots + x_{n}^{2}}{n}}$

$H_{n}\leq G_{n}\leq A_{n}\leq Q_{n} $