Category:Cauchy's Mean Theorem
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This category contains pages concerning Cauchy's Mean Theorem:
Let $x_1, x_2, \ldots, x_n \in \R$ be real numbers which are all positive.
Let $A_n$ be the arithmetic mean of $x_1, x_2, \ldots, x_n$.
Let $G_n$ be the geometric mean of $x_1, x_2, \ldots, x_n$.
Then:
- $A_n \ge G_n$
with equality holding if and only if:
- $\forall i, j \in \set {1, 2, \ldots, n}: x_i = x_j$
That is, if and only if all terms are equal.
Pages in category "Cauchy's Mean Theorem"
The following 6 pages are in this category, out of 6 total.