query: How to evaluate: $\lim_{n\to\infty} \left(\frac{1^n+2^n+3^n+\cdots+n^n}{n^n}\right)\,?$
positive_passages.docid: 37148
positive_passages.text: How to evaluate $ \lim \limits_{n\to \infty} \sum \limits_ {k=1}^n \frac{k^n}{n^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: 73670
negative_passages.text: Help with Limit: $\lim_{n \to \infty} \frac{(2 n)! e^n (n)^n}{n! (2 n)^{2 n}}$
negative_passages.docid: 67500
negative_passages.text: Sum of $\lim_{n\rightarrow \infty}\left(\frac{n}{n^2+1}+\frac{n}{n^2+2}+\cdots \cdots \cdots +\frac{n}{n^2+n}\right)$
negative_passages.docid: 115819
negative_passages.text: Evaluate $\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n})$
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: 56265
negative_passages.text: limit $\lim\limits_{n\to\infty}\left(\sum\limits_{i=1}^{n}\frac{1}{\sqrt{i}} - 2\sqrt{n}\right)$
negative_passages.docid: 63672
negative_passages.text: Understanding a particular evaluation of $\prod\limits_{n=2}^{\infty}\left(1-\frac{1}{n^3}\right)$
negative_passages.docid: 11389
negative_passages.text: What is $\lim_{n\to \infty}\sum_{k=1}^n \left(\frac{k}{n}\right)^n$?
negative_passages.docid: 4644
negative_passages.text: Finding the limit $\lim \limits_{n \to \infty}\ (\cos \frac x 2 \cdot\cos \frac x 4\cdot \cos \frac x 8\cdots \cos \frac x {2^n}) $
negative_passages.docid: 111418
negative_passages.text: Finding lim${_{n \rightarrow \infty}}\left( \frac{n^3}{2^n} \right)$
negative_passages.docid: 65137
negative_passages.text: Evaluating $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ where $a_1 \ge \cdots\ge a_k \ge 0$
negative_passages.docid: 35169
negative_passages.text: Finding the limit of $\left(\frac{n}{n+1}\right)^n$
negative_passages.docid: 50398
negative_passages.text: Limit $\lim\limits_{n\to\infty}\left(\frac{n}{n^2+1}+\frac{n}{n^2+2}+\frac{n}{n^2+3}+\cdots+\frac{n}{n^2+n}\right)$
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: 154286
negative_passages.text: Evaluating $\lim_{n \to \infty} (1 + 1/n)^{n}$
negative_passages.docid: 155353
negative_passages.text: Find the limit of $ a_n =\left(1+\frac{1^2}{n^2}\right)^1\left(1+\frac{2^2}{n^2}\right)^2\cdots \left(1+\frac{n^2}{n^2}\right)^n$