Root-mean power: Difference between revisions
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A root mean power can be expressed as <cmath>\sqrt[n]{\frac{x_1^n+\cdots+x_a^n}{a}}</cmath> where <math>n</math> is the root mean power and the mean is bigger when <math>n</math> is bigger. As <math>n</math> reaches <math>-\infty</math>, the mean reaches the lowest number. As <math>n</math> reaches <math>\infty</math>, the mean reaches the highest number. Examples and their powers: Cubic Mean: 3, Quadratic Mean: 2, Arithmetic Mean: 1, Geometric Mean: 0 (theoretical, can't be solved using radicals), Harmonic Mean: -1 | A root mean power can be expressed as <cmath>\sqrt[n]{\frac{x_1^n+\cdots+x_a^n}{a}}</cmath> where <math>n</math> is the root mean power and the mean is bigger when <math>n</math> is bigger. As <math>n</math> reaches <math>-\infty</math>, the mean reaches the lowest number. As <math>n</math> reaches <math>\infty</math>, the mean reaches the highest number. Examples and their powers: Cubic Mean: 3, Quadratic Mean: 2, Arithmetic Mean: 1, Geometric Mean: 0 (theoretical, can't be solved using radicals), Harmonic Mean: -1 | ||
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Latest revision as of 00:01, 2 November 2023
A root mean power can be expressed as ![\[\sqrt[n]{\frac{x_1^n+\cdots+x_a^n}{a}}\]](http://latex.artofproblemsolving.com/e/9/f/e9f31f4f742327a81eacc360154358df6321959d.png)
where 
is the root mean power and the mean is bigger when is bigger. As reaches 
, the mean reaches the lowest number. As reaches 
, the mean reaches the highest number. Examples and their powers: Cubic Mean: 3, Quadratic Mean: 2, Arithmetic Mean: 1, Geometric Mean: 0 (theoretical, can't be solved using radicals), Harmonic Mean: -1
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