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AM GM Inequality

AM-GM Inequality

Oct 29, 20231 min read

Math

$\frac{a _{1} + \dots + a _{n}}{n} \geq n a_{1} \dots a_{n}$

The arithmetic mean of a list of positive numbers is greater than or equal to those numbers’ geometric mean

$a^{2} + b^{2} \geq 2 ab \forall a, b \geq 0$

Graph View

$\displaystyle \frac{a_{1}+\ldots+a_{n}}{n}\geq\sqrt[n]{ a_{1}\ldots a_{n} }$
$\displaystyle a^{2}+b^{2}\geq 2ab~\forall~a,b\geq0$

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