query: Prove the inequality....
positive_passages.docid: 104498
positive_passages.text: Show that $x^3y^3(x^3+y^3) \leq 2$
negative_passages.docid: 116206
negative_passages.text: Complex number question on proving an inequality.
negative_passages.docid: 40936
negative_passages.text: How prove this integral inequality
negative_passages.docid: 129890
negative_passages.text: Proving inequality $|\sin(n\theta) |\le n\sin\theta$
negative_passages.docid: 105268
negative_passages.text: prove inequality through mean value theorem
negative_passages.docid: 120093
negative_passages.text: Proof of inequality $2(\sqrt{n+1}-\sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n} - \sqrt{n-1})$ using induction
negative_passages.docid: 25458
negative_passages.text: Prove inequalities $2\sqrt{n+1}-2 \leq 1 + 1/\sqrt{2} + 1/\sqrt{3} + .... + 1/\sqrt{n}\leq 2\sqrt{n}-1$
negative_passages.docid: 78144
negative_passages.text: How to prove the inequality $a_1^{a_1}a_2^{a_2}\cdots a_n^{a_n} > \left(\frac{a_1+\dots+a_n}{n}\right)^{a_1+\dots+a_n}$?
negative_passages.docid: 8007
negative_passages.text: Proof of Young's inequality
negative_passages.docid: 29198
negative_passages.text: How to prove the following inequality $|\prod_{i=1}^{i=n}a_i-\prod_{i=1}^{i=n}b_i| < n\delta$?
negative_passages.docid: 30386
negative_passages.text: Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
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: 96217
negative_passages.text: If a and b are non-negative real numbers then demonstrate inequality
negative_passages.docid: 16798
negative_passages.text: Prove the inequality $n! \geq 2^n$ by induction
negative_passages.docid: 16524
negative_passages.text: Proof of an inequality by induction: $(1 + x_1)(1 + x_2)...(1 + x_n) \ge 1 + x_1 + x_2 + ... + x_n$
negative_passages.docid: 40700
negative_passages.text: Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$
negative_passages.docid: 77026
negative_passages.text: Proof with inequalities