query: Proof of Jensen's inequality without the use of induction
positive_passages.docid: 116781
positive_passages.text: Could someone give a detailed (yet elementary) proof for Jensen's inequality?
negative_passages.docid: 24617
negative_passages.text: Proof of Inequality using AM-GM
negative_passages.docid: 13228
negative_passages.text: Proofs of AM-GM inequality
negative_passages.docid: 128189
negative_passages.text: Proving Integral Inequality
negative_passages.docid: 7404
negative_passages.text: Induction and convergence of an inequality: $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\leq \frac{1}{\sqrt{2n+1}}$
negative_passages.docid: 108704
negative_passages.text: Help with proof of $|x+y| \geq |x|-|y|$
negative_passages.docid: 30783
negative_passages.text: Prove inequality $n<3^n$ using mathematical induction
negative_passages.docid: 16798
negative_passages.text: Prove the inequality $n! \geq 2^n$ by induction
negative_passages.docid: 25738
negative_passages.text: Jensen's Inequality implies convexity?
negative_passages.docid: 32427
negative_passages.text: Basic mathematical induction regarding inequalities
negative_passages.docid: 42285
negative_passages.text: Prove by mathematical induction.
negative_passages.docid: 80556
negative_passages.text: Demonstrate by induction the inequality: $\ln(1+n)\leq\sum_{i=1}^{n}\frac{1}{i}\leq1+\ln(n)$
negative_passages.docid: 126632
negative_passages.text: Proving Inequalities with Absolute values
negative_passages.docid: 51877
negative_passages.text: Why is this 'Proof' by induction not valid?
negative_passages.docid: 22237
negative_passages.text: Proof of triangle inequality
negative_passages.docid: 118613
negative_passages.text: Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
negative_passages.docid: 91740
negative_passages.text: Hadamard's inequality proof