# Difference between revisions of "Titu's Lemma"

Mathletema (talk | contribs) (Created page with "Titu's lemma states that: <cmath> \frac{ a_1^2 } { b_1 } + \frac{ a_2 ^2 } { b_2 } + \cdots + \frac{ a_n ^2 } { b_n } \geq \frac{ (a_1 + a_2 + \cdots+ a_n ) ^2 } { b_1 + b_2...") |
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<cmath> \frac{ a_1^2 } { b_1 } + \frac{ a_2 ^2 } { b_2 } + \cdots + \frac{ a_n ^2 } { b_n } \geq \frac{ (a_1 + a_2 + \cdots+ a_n ) ^2 } { b_1 + b_2 + \cdots+ b_n }. </cmath> | <cmath> \frac{ a_1^2 } { b_1 } + \frac{ a_2 ^2 } { b_2 } + \cdots + \frac{ a_n ^2 } { b_n } \geq \frac{ (a_1 + a_2 + \cdots+ a_n ) ^2 } { b_1 + b_2 + \cdots+ b_n }. </cmath> | ||

− | It is a direct consequence of Cauchy-Schwarz theorem | + | It is a direct consequence of Cauchy-Schwarz theorem. |

+ | |||

+ | Titu's lemma is named after Titu Andreescu, and is also known as T2 lemma, Engel's form, or Sedrakyan's inequality. |

## Latest revision as of 18:19, 11 October 2019

Titu's lemma states that:

It is a direct consequence of Cauchy-Schwarz theorem.

Titu's lemma is named after Titu Andreescu, and is also known as T2 lemma, Engel's form, or Sedrakyan's inequality.