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Let $A$ be the arithmetic mean of set $s$, $G$ be the geometric mean, and $H$ be the harmonic mean.

I know that when there are two terms in a set, $G=\sqrt{AH}$. However, is there an equation like this for when there are more than two terms?

I am aware of the A.M-G.M-H.M inequality that states that $H<G<A$. However, I am looking for an equation.

4yl1n
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    I don't think we should expect an equation when the number of variables matches or exceeds how many functions of them you're talking about - we should expect $(H,G,A)$ to carve out some 3D region defined by inequalities. I suppose the question to ask is if $0<H<G<A$ sufficient to describe the region for means of positive values. – anon Apr 13 '20 at 03:02

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