query: Prove $\left\|x\right\|_2\leq\sqrt{n}\left\|x\right\|_\infty$
positive_passages.docid: 148582
positive_passages.text: Proof: $\|X\|_2\leq \sqrt{n}\|X\|_\infty$
negative_passages.docid: 76756
negative_passages.text: A convergence proof: $\lim_{n\to\infty} \left(1+n^2\right)^{\frac1n}$
negative_passages.docid: 97558
negative_passages.text: Prove that $\left| f'(x)\right| \leq \sqrt{2AC}$ using integration
negative_passages.docid: 52331
negative_passages.text: What is $\lim_{n\to \infty }\left(\sqrt[\leftroot{-2}\uproot{2}n+1]{(n+1)!}-\sqrt[\leftroot{-2}\uproot{2}n]{n!}\right)$?
negative_passages.docid: 42976
negative_passages.text: How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
negative_passages.docid: 13125
negative_passages.text: Convergence of $\sum_{n=1}^\infty{\left(\sqrt[n]{n}-1\right)}$
negative_passages.docid: 66387
negative_passages.text: Prove $(x_1+.....+x_n)^2 \leq n(x_1^2 + .....+x_n^2)$
negative_passages.docid: 65662
negative_passages.text: Prove $\forall K > 0: \lim_{n\rightarrow\infty} \sqrt[n]{K} = 1$
negative_passages.docid: 22575
negative_passages.text: Prove that $\lim\limits_{n\rightarrow\infty} \left(1+\frac{1}{a_{n}} \right)^{a_{n}}=e$ if $\lim\limits_{n\rightarrow\infty} a_{n}=\infty$
negative_passages.docid: 42842
negative_passages.text: Proof for $\epsilon$ closeness to $\sqrt{2}$ for all values of $\epsilon$
negative_passages.docid: 66247
negative_passages.text: Proving inequality $\left( \frac {x} {y}\right) ^{x}\left( \frac {1-x} {1-y}\right) ^{1-x}\geqslant 1$
negative_passages.docid: 140409
negative_passages.text: Prove that $\sqrt{n} > \ln n$
negative_passages.docid: 29679
negative_passages.text: Prove: $|x-y|\leq |x|+|y|$
negative_passages.docid: 61162
negative_passages.text: Show that $\left(\int_0^1 f(x)\,dx\right)^2\leq2\int_0^1x\, f(x)^2\,dx $
negative_passages.docid: 145423
negative_passages.text: prove that if $1 \le m \le n$ then $\left(1+\frac1n\right)^m < 1+\frac mn + \left(\frac mn\right)^2$
negative_passages.docid: 136403
negative_passages.text: Prove that $\sqrt{a}\leq\frac{1+a}{2}$
negative_passages.docid: 139215
negative_passages.text: Find the value of $\lim_{x \to - \infty} \left( \sqrt{x^2 + 2x} - \sqrt{x^2 - 2x} \right)$