query: Evaluate $\lim_{n\to\infty}\frac{1^{k}+2^{k}+...+n^{k}}{n^{k+1}}$
positive_passages.docid: 17872
positive_passages.text: Evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}}$
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: 37260
negative_passages.text: Calculate $\lim_{n\to{+}\infty}{(\sqrt{n^{2}+n}-n)}$
negative_passages.docid: 60104
negative_passages.text: Evaluate $\sum_{k=1}^\infty\frac{x^k}{k(k+1)}$
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: 51231
negative_passages.text: Find the limit of $\frac{n^{x}}{(1 + x)^{n}}$
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: 154506
negative_passages.text: Evaluating $\lim_{n\rightarrow\infty} (\frac{(1+\frac{1}{n})^n}{e})^n$
negative_passages.docid: 8387
negative_passages.text: Evaluate $\lim_{n \rightarrow \infty} \frac {[(n+1)(n+2)\cdots(n+n)]^{1/n}}{n}$
negative_passages.docid: 4578
negative_passages.text: Evaluate the value of $\lim_{n \to \infty}\frac{x_n}{\prod_{i=1}^{n-1} x_i}$ where $x_n=x_{n-1}^2-2, x_1=5$
negative_passages.docid: 114481
negative_passages.text: Calculating $\lim_{n\to\infty}\sqrt[n]{2^n-n^2}$
negative_passages.docid: 28666
negative_passages.text: simple convergence test $\lim_{n \to \infty} \frac{2^{n+1}+3^{n+1}}{2^n+3^n}$
negative_passages.docid: 84595
negative_passages.text: How to evaluate $\lim\limits_{n\to+\infty} \prod\limits_{k=1}^n (1+k/n^2)$?
negative_passages.docid: 101716
negative_passages.text: Find this limit: $ \lim_{n \to \infty}{(e^{\frac{1}{n}} - \frac{2}{n})^n}$
negative_passages.docid: 137155
negative_passages.text: Sum $ \sum\limits_{k=1}^{\infty} \frac{k^2}{2^k}$
negative_passages.docid: 61300
negative_passages.text: Evaluating $\lim\limits_{n\to\infty} \left(\frac{1^p+2^p+3^p + \cdots + n^p}{n^p} - \frac{n}{p+1}\right)$
negative_passages.docid: 146663
negative_passages.text: Limit $\lim_{n \to \infty} \frac {a_n}{2^{n-1}}=\frac 4{\pi}$ for $a_{n+1}=a_n+\sqrt{1+a_n^2}$ and $a_0=0$