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Note: Regarding the application of Jensen's inequality in high school, π has been introduced in the previous tweet. Link: Issue 748 [Derivative] Application of Jensen's inequality in high school. Interested students can go to the above link. Finally, according to Jensen's inequality: [Lemma 3] For any positive definite matrix r>0, and all continuously differentiable vector functions \omega: Consider the jensen inequality \left (\sum_ {i=1}^k\frac {a_i} {\sum_ {j=1}^k a_j} x_i\right)^n\le\sum_ {i=1}^k \frac {a_i} {\sum_ {j=1}^k a_j} x_i^n\\ i.e.

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Weighted jensen inequality: Assume \lambda _ {i}\in r^ {+} and \sum_ {i=1}^ {n} {\lambda_i}=1 , f (x) is a strictly downward convex function in the interval (a,b), then for all x_ {1},x_ {2},.,x_ {n} in (a,b), there is

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