query: Compute $\lim_{n\to\infty}(a_1^n+a_2^n+...+a_r^n)^{1/n}$.
positive_passages.docid: 83318
positive_passages.text: How to compute the limit $\lim_{n \to \infty} \sqrt[n]{a_1^n + \cdots + a_m^n}$?
negative_passages.docid: 41366
negative_passages.text: Compute $\lim\limits_{n\to\infty} \left(1+\frac{1}{n}\right)\left(1+\frac{2}{n}\right)^{{1}/{2}}\cdots\left(1+\frac{n}{n}\right)^{{1}/{n}}$
negative_passages.docid: 47606
negative_passages.text: Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit
negative_passages.docid: 29901
negative_passages.text: Computing $\lim_{n\rightarrow \infty} \frac{1+\sqrt{2}+\sqrt[3]{3}+\cdots+\sqrt[n]{n}}{n}$.
negative_passages.docid: 95718
negative_passages.text: Computing $ \lim_{n\rightarrow \infty}\left(\frac{1^n+2^n+\cdots \cdots +n^n}{n^n}\right)$
negative_passages.docid: 25193
negative_passages.text: Find $ \lim _{n\to \infty} \frac{n^1+\dots+n^n}{1^n+\dots+n^n}$
negative_passages.docid: 17438
negative_passages.text: Evaluate $\lim_{n\to \infty} \sum_{r=1}^n \frac {1}{2^r}\tan \left(\frac {1}{2^r}\right)$
negative_passages.docid: 79256
negative_passages.text: How should I calculate $\lim_{n\rightarrow \infty} \frac{1^n+2^n+3^n+...+n^n}{n^n}$
negative_passages.docid: 61698
negative_passages.text: Evaluate the limit $\lim\limits_{n \to \infty} \frac{1}{1+n^2} +\frac{2}{2+n^2}+ \ldots +\frac{n}{n+n^2}$
negative_passages.docid: 30063
negative_passages.text: How do you calculate this limit $\lim_{n\to\infty}\sum_{k=1}^{n} \frac{k}{n^2+k^2}$?
negative_passages.docid: 156231
negative_passages.text: Computing $\lim\limits_{n\to\infty} \int_{0}^{\infty}\frac{\sin(x/n)}{(1+x/n)^{n}}\, dx$
negative_passages.docid: 16634
negative_passages.text: How to show $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$?
negative_passages.docid: 79646
negative_passages.text: Compute $\lim_{n\to\infty}\frac{\tfrac{n}{1}+\tfrac{n-1}{2}+\dots+\tfrac{2}{n-1}+\tfrac{1}{n}}{\ln(n!)}$
negative_passages.docid: 54775
negative_passages.text: Find $\lim_{n \to \infty} n[(1+\frac{1}{n})^n - e]$
negative_passages.docid: 97571
negative_passages.text: Find the limit $ \lim_{n\to \infty} 2^{\frac{1}{n}}$
negative_passages.docid: 45737
negative_passages.text: Limit $\lim_{n \to \infty} \frac{n!}{n^n}$
negative_passages.docid: 142778
negative_passages.text: Finding $\lim_{n\to\infty}a_n$ if $a_0=a,a_1=b$ and $a_n=\frac{1}{2}(a_{n-1}+a_{n-2})$ where $a, b \in \mathbb{R}$