query: finding value of $\lim_{n\rightarrow \infty}\sqrt[n]{\frac{(27)^n(n!)^3}{(3n)!}}$
positive_passages.docid: 153269
positive_passages.text: Find $\lim_{n \to \infty} \left( \frac{3^{3n}(n!)^3}{(3n)!}\right)^{1/n}$
negative_passages.docid: 154506
negative_passages.text: Evaluating $\lim_{n\rightarrow\infty} (\frac{(1+\frac{1}{n})^n}{e})^n$
negative_passages.docid: 50243
negative_passages.text: Find $\lim_{n \to +\infty} \frac{1}{n}\sqrt[n]{\frac{(2n)!}{n!}} $ using Riemann integral
negative_passages.docid: 35169
negative_passages.text: Finding the limit of $\left(\frac{n}{n+1}\right)^n$
negative_passages.docid: 114481
negative_passages.text: Calculating $\lim_{n\to\infty}\sqrt[n]{2^n-n^2}$
negative_passages.docid: 129987
negative_passages.text: Find $\lim\frac{1}{\sqrt{n}}\left(\frac{1}{\sqrt{1}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\ldots+\frac{1}{\sqrt{2n-1}+\sqrt{2n+1}}\right)$
negative_passages.docid: 41203
negative_passages.text: Finding $\lim\limits_{x \to \infty} (\sqrt{9x^2+x} - 3x)$
negative_passages.docid: 19631
negative_passages.text: Finding $\lim_{n\to \infty}\sqrt n \int_0^1 \frac{\,dx}{(1+x^2)^n}$
negative_passages.docid: 46103
negative_passages.text: Compute: $\lim_{n \rightarrow \infty}\sqrt{n}(A_{n+1} − A_n)$ where $A_n = \frac{1}{n}(a_1 + a_2 + \cdots + a_n)$
negative_passages.docid: 76638
negative_passages.text: Find the limit $ \lim_{n \to \infty}\left(\frac{a^{1/n}+b^{1/n}+c^{1/n}}{3}\right)^n$
negative_passages.docid: 110588
negative_passages.text: Showing $\lim_{n\rightarrow\infty}\sqrt[3]{n^3+n^2}-\sqrt[3]{n^3+1}\rightarrow\frac{1}{3}$
negative_passages.docid: 20773
negative_passages.text: Find $\lim\limits_{n \to \infty} \frac{\sqrt 1 + \sqrt 2 + \dots + \sqrt{n}}{n\sqrt{n}}$.
negative_passages.docid: 125538
negative_passages.text: limit of $n^{\frac{1}{\sqrt{n}}}$
negative_passages.docid: 8489
negative_passages.text: How to compute $\lim_{n\rightarrow\infty}\frac1n\left\{(2n+1)(2n+2)\cdots(2n+n)\right\}^{1/n}$
negative_passages.docid: 139215
negative_passages.text: Find the value of $\lim_{x \to - \infty} \left( \sqrt{x^2 + 2x} - \sqrt{x^2 - 2x} \right)$
negative_passages.docid: 101027
negative_passages.text: What is the value of lim$_{n\to \infty} a_n$ if $\lim_{n \to \infty}\left|a_n+ 3\left(\frac{n-2}{n}\right)^n \right|^{\frac{1}{n}}=\frac{3}{5}$?
negative_passages.docid: 5521
negative_passages.text: Evalute $ \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)} $