The Infamous Inequality

$\displaystyle \sum_{i=1}^n \dfrac{a_i}{n}=\dfrac{a_1+a_2+a_3+\ldots+a_n}{n}$ is the arithmetic mean of a set of values

$\displaystyle \prod_{i=1}^n \sqrt[n]{a_i}=\sqrt[n]{a_1a_2a_3\ldots a_n}$ is the geometric mean of a set of values

By the AM-GM inequality , we know that AM $\geq$ GM, that is

$\displaystyle \sum_{i=1}^n \dfrac{a_i}{n} \geq \prod_{i=1}^n \sqrt[n]{a_i}$

Therefore, the answer is $\boxed{\text{False}}$

The inequality sign is reversed.

See AM-GM inequality