query: A combinatorial inequality
positive_passages.docid: 2708
positive_passages.text: Inequality ${n \choose k} \leq \left(\frac{en}{ k}\right)^k$
negative_passages.docid: 65983
negative_passages.text: Combinatorial proof of binomial coefficient summation identity
negative_passages.docid: 16392
negative_passages.text: Prove the Inequality on sequence
negative_passages.docid: 11983
negative_passages.text: Proof of Clarkson's Inequality
negative_passages.docid: 156669
negative_passages.text: Trying to prove a simple (?) inequality
negative_passages.docid: 95901
negative_passages.text: Inequality similar to the Schwarz-Pick theorem
negative_passages.docid: 138304
negative_passages.text: getting tight bounds on n!
negative_passages.docid: 24212
negative_passages.text: proving how many permutations exist.
negative_passages.docid: 49783
negative_passages.text: A possible inequality related to binomial theorem (or, convex/concave functions)
negative_passages.docid: 136694
negative_passages.text: Probabilistic Proof of Kraft-Mcmillan Inequality
negative_passages.docid: 149216
negative_passages.text: Give a combinatorial proof to show the following for all integers $n \geq 2$.
negative_passages.docid: 14986
negative_passages.text: Proving a combinatorics equality: $\binom{r}{r} + \binom{r+1}{r} + \cdots + \binom{n}{r} = \binom{n+1}{r+1}$
negative_passages.docid: 118244
negative_passages.text: An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
negative_passages.docid: 131596
negative_passages.text: Symmetric Inequality in $\mathbb{R}$
negative_passages.docid: 26828
negative_passages.text: Generalization of Hölder inequality
negative_passages.docid: 69748
negative_passages.text: Semi-Ambiguous Combinatorics Problem
negative_passages.docid: 126032
negative_passages.text: Proving a certain inequality