query: Help to prove an inequality not by math induction
positive_passages.docid: 7404
positive_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: 105268
negative_passages.text: prove inequality through mean value theorem
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: 32149
negative_passages.text: Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
negative_passages.docid: 42285
negative_passages.text: Prove by mathematical induction.
negative_passages.docid: 40420
negative_passages.text: Proof by induction of Bernoulli's inequality: $(1 + x)^n \geq 1 + nx$
negative_passages.docid: 23264
negative_passages.text: Inequality $ \vert \sqrt{a}-\sqrt{b} \vert \leq \sqrt{ \vert a -b \vert } $
negative_passages.docid: 19078
negative_passages.text: Prove an interpolation inequality
negative_passages.docid: 66996
negative_passages.text: Proof by induction of Bernoulli's inequality $ (1+x)^n \ge 1+nx$
negative_passages.docid: 8207
negative_passages.text: Can I prove this inequality algebraically?
negative_passages.docid: 15232
negative_passages.text: Proving an inequality involving real powers
negative_passages.docid: 81800
negative_passages.text: Prove inequality using Jensen's inequality
negative_passages.docid: 90343
negative_passages.text: Proving the inequality $|e^z-1|\leq e^{|z|}-1$
negative_passages.docid: 51730
negative_passages.text: How to prove this inequality $3^{n}\geq n^{2}$ for $n\geq 1$ with mathematical induction?
negative_passages.docid: 121107
negative_passages.text: Proof by induction: $n^{n+1} > (n + 1)^n$, $(1 + x)^n \ge 1 + nx$, other inequalities
negative_passages.docid: 156669
negative_passages.text: Trying to prove a simple (?) inequality
negative_passages.docid: 138490
negative_passages.text: An inequality with a weird condition