query: Prove the inequality
positive_passages.docid: 35719
positive_passages.text: Prove that $\frac{a}{a^2+1}+\frac{b}{b^2+1}+\frac{c}{c^2+1} \leq \frac{9}{10}$ if $a+b+c=1$.
negative_passages.docid: 7775
negative_passages.text: Show that $|x-y|\leq |x|+|y|$.
negative_passages.docid: 110153
negative_passages.text: How to prove this inequality?$\frac{1}{n+1} + \frac{1}{n+2} + \cdots+\frac{1}{n+n} + \frac{1}{4n} > \ln 2$
negative_passages.docid: 65168
negative_passages.text: Proof of sequence inequality
negative_passages.docid: 96217
negative_passages.text: If a and b are non-negative real numbers then demonstrate inequality
negative_passages.docid: 81618
negative_passages.text: Prove $||a|-|b| | \leq |a-b|$
negative_passages.docid: 16798
negative_passages.text: Prove the inequality $n! \geq 2^n$ by induction
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: 139711
negative_passages.text: prove this inequality with $\sum\limits_\text{cyc}\sqrt{1-xy}\ge 2$
negative_passages.docid: 73987
negative_passages.text: Prove the inequality $({1+\frac{a}b})^n$ + $(1+\frac{b}a)^n$ $\geq$ $2^{n+1}$
negative_passages.docid: 115335
negative_passages.text: How can we prove this integral inequality?
negative_passages.docid: 126557
negative_passages.text: Proving the inequality $\sum_{\text{cyc}} \frac{a}{a^2+b^3+c^3}\le\frac1{5abc}$
negative_passages.docid: 8007
negative_passages.text: Proof of Young's inequality
negative_passages.docid: 68986
negative_passages.text: Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$
negative_passages.docid: 3316
negative_passages.text: Prove QM-AM inequality
negative_passages.docid: 91871
negative_passages.text: Proving quadratic inequalities?
negative_passages.docid: 142785
negative_passages.text: How can I prove Holder inequality for $0<p<1$?