query: The exact value of $\lim_{n \to \infty} \frac{a_n}{\sqrt[4]{n^3}}$
positive_passages.docid: 155695
positive_passages.text: The convergence of a sequence
negative_passages.docid: 17090
negative_passages.text: Compute $\lim_\limits{n\to\infty}a_n$ where $a_{n+2}=\sqrt{a_n.a_{n+1}}$
negative_passages.docid: 4638
negative_passages.text: What is the value of $\lim_{n\to \infty} \sum_{j=n}^{4n} {4n \choose j}\bigl(\frac{1}{4}\bigr)^{j} \bigl(\frac{3}{4}\bigr)^{4n-j}$?
negative_passages.docid: 33976
negative_passages.text: Prove that $\lim_{n \to \infty} \sqrt[n]{a} = 1$ using only the basic properties of sequences
negative_passages.docid: 144273
negative_passages.text: Find $\lim_{n\to\infty} \frac{1}{n} \int_0^\infty f(x) e^{-a_n x} dx$
negative_passages.docid: 107953
negative_passages.text: Limit of the sequence $\lim_{n\rightarrow\infty}\sqrt[n]n$
negative_passages.docid: 66526
negative_passages.text: Find the limit of: $\lim_{n\to\infty} \frac{1}{\sqrt[n+1]{(n+1)!} - \sqrt[n]{(n)!}}$
negative_passages.docid: 133244
negative_passages.text: Finding $\lim_{n \to \infty} n(\sqrt[n]{2} - 1)$
negative_passages.docid: 81090
negative_passages.text: Calculate $\lim_{n\to\infty}(\sqrt{n^2+n}-n)$.
negative_passages.docid: 7
negative_passages.text: Find value of the limit: $\lim_{n\to \infty}\sqrt[n]{1^2+2^2+\cdots+n^2}$
negative_passages.docid: 37260
negative_passages.text: Calculate $\lim_{n\to{+}\infty}{(\sqrt{n^{2}+n}-n)}$
negative_passages.docid: 45737
negative_passages.text: Limit $\lim_{n \to \infty} \frac{n!}{n^n}$
negative_passages.docid: 37394
negative_passages.text: How to find $\lim\limits_{n\to\infty} n·(\sqrt[n]{a}-1)$?
negative_passages.docid: 31889
negative_passages.text: The limit as $n$ approaches infinity of $n(a^{1/n}-1)$
negative_passages.docid: 97571
negative_passages.text: Find the limit $ \lim_{n\to \infty} 2^{\frac{1}{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: 114481
negative_passages.text: Calculating $\lim_{n\to\infty}\sqrt[n]{2^n-n^2}$