HM-GM-AM-QM inequalities (Q2312489)

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mathematical relationships

• power mean inequality
• QAGH inequality
• QAGH

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Language	Label	Description	Also known as
English	HM-GM-AM-QM inequalities	mathematical relationships	power mean inequality QAGH inequality QAGH

Statements

instance of

inequation

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theorem

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defining formula

${\displaystyle {\dfrac {n}{\displaystyle \sum _{i=1}^{n}{\dfrac {1}{x_{i}}}}}\leq {\sqrt[{n}]{\prod _{i=1}^{n}x_{i}}}\leq {\dfrac {\displaystyle \sum _{i=1}^{n}x_{i}}{n}}\leq {\sqrt {\dfrac {\displaystyle \sum _{i=1}^{n}x_{i}^{2}}{n}}}}$

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in defining formula

${\displaystyle {\dfrac {n}{\displaystyle \sum _{i=1}^{n}{\dfrac {1}{x_{i}}}}}}$

symbol represents

harmonic mean

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${\displaystyle {\sqrt[{n}]{\prod _{i=1}^{n}x_{i}}}}$

symbol represents

geometric mean

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${\displaystyle {\dfrac {\displaystyle \sum _{i=1}^{n}x_{i}}{n}}}$

symbol represents

arithmetic mean

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${\displaystyle {\sqrt {\dfrac {\displaystyle \sum _{i=1}^{n}x_{i}^{2}}{n}}}}$

symbol represents

root mean square

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

Brilliant Wiki ID

power-mean-qagh

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Google Knowledge Graph ID

/g/122wblqm

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/g/11fjn2mq2x

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/g/12lngw7cx

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Sitelinks

Wikipedia(5 entries)

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• cswiki Nerovnosti mezi průměry
• enwiki QM-AM-GM-HM inequalities
• glwiki Desigualdades QM-AM-GM-HM
• nlwiki HM-GM-AM-QM
• zhwiki 平均数不等式

Wikibooks(0 entries)

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Wikinews(0 entries)

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Wikiquote(0 entries)

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Wikisource(0 entries)

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Wikiversity(0 entries)

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Wikivoyage(0 entries)

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Wiktionary(0 entries)

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Multilingual sites(0 entries)

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