一般地，假設 a 1 , a 2 , ⋯ , a n {\displaystyle a_{1},a_{2},\cdots ,a_{n}} 為n個非負實數,它們的算術平均值記為
A n = a 1 + a 2 + ⋯ + a n n {\displaystyle \mathbf {A} _{n}={\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}}
幾何平均值記為
G n = a 1 ⋅ a 2 ⋯ a n n {\displaystyle \mathbf {G} _{n}={\sqrt[{n}]{a_{1}\cdot a_{2}\cdots a_{n}}}}
則
A n ⩾ G n {\displaystyle A_{n}\geqslant G_{n}}
當且僅 a 1 = a 2 = ⋯ = a n {\displaystyle a_{1}=a_{2}=\cdots =a_{n}} 時,等號成立.
上述不等式即為平均值不等式，簡稱均值不等式
為n個非負實數,它們的算術平均值記為
![{\displaystyle \mathbf {G} _{n}={\sqrt[{n}]{a_{1}\cdot a_{2}\cdots a_{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a9c9a16dcb65dd4915a726b9d6b0951add5c7384)
時,等號成立.
