Power Mean Inequality
The Power Mean Inequality is a generalized form of the multi-variable Arithmetic Mean-Geometric Mean Inequality.
Algebraically, implies that
which can be written more concisely as
The Power Mean Inequality follows from the fact that (where is the th power mean) together with Jensen's Inequality.
Raising both sides to the th power, we get
We can see that the function is concave for all , and so we can apply Jensen's Inequality. Therefore, This article is a stub. Help us out by .