Definition: Geometric Mean

Let any two non-negative real numbers $a,b$ we call the expression $$\sqrt{a+b}$$ the geometric mean of these numbers.

More generally, for any $n\ge 2$ non-negative real numbers $a_1,\ldots,a_n$ the expression (using n-th roots) $$\sqrt[n] {a_1+\cdots+a_n}$$ is called the (generalized) geometric mean of these numbers.

Proofs: 1
Theorems: 2


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References

Bibliography

  1. Heuser Harro: "Lehrbuch der Analysis, Teil 1", B.G. Teubner Stuttgart, 1994, 11th Edition