TOPICS
Search

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

Explore with Wolfram|Alpha

Cite this as:

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

Subject classifications