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Cauchy's Formula

The geometric mean is smaller than the arithmetic mean,

(product_(i=1)^Nn_i)^(1/N)<=(sum_(i=1)^(N)n_i)/N,

with equality in the cases (1) N=1 or (2) n_i=n_j for all i,j.

See also

Arithmetic Mean, Geometric Mean

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Cite this as:

Weisstein, Eric W. "Cauchy's Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CauchysFormula.html

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