query: Prove an inequality using Jensen's
positive_passages.docid: 25648
positive_passages.text: Prove $(a_1+b_1)^{1/n}\cdots(a_n+b_n)^{1/n}\ge \left(a_1\cdots a_n\right)^{1/n}+\left(b_1\cdots b_n\right)^{1/n}$
negative_passages.docid: 35001
negative_passages.text: Prove inequality using Schwarz's Lemma
negative_passages.docid: 105268
negative_passages.text: prove inequality through mean value theorem
negative_passages.docid: 155232
negative_passages.text: Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
negative_passages.docid: 131180
negative_passages.text: When Jensen's inequality is equality
negative_passages.docid: 23264
negative_passages.text: Inequality $ \vert \sqrt{a}-\sqrt{b} \vert \leq \sqrt{ \vert a -b \vert } $
negative_passages.docid: 116460
negative_passages.text: How to prove this inequality using Taylor approximation?
negative_passages.docid: 116781
negative_passages.text: Could someone give a detailed (yet elementary) proof for Jensen's inequality?
negative_passages.docid: 143801
negative_passages.text: Proving the AGM inequality with 3 variables
negative_passages.docid: 156669
negative_passages.text: Trying to prove a simple (?) inequality
negative_passages.docid: 118559
negative_passages.text: Prove the inequality $\sum_{1\le i<j\le n}\sqrt{a_ia_j}<\frac{n-1}2\sum_{i=1}^n a_i$
negative_passages.docid: 23119
negative_passages.text: An application of Jensen's Inequality
negative_passages.docid: 103806
negative_passages.text: How to prove triangle inequality for $p$-norm?
negative_passages.docid: 135550
negative_passages.text: Inequality question­
negative_passages.docid: 117262
negative_passages.text: Proving a logarithm inequality
negative_passages.docid: 5430
negative_passages.text: Using Cauchy's integral theorem to prove a inequality
negative_passages.docid: 20863
negative_passages.text: how do I prove this inequallity?