query: Limit of $(n+n^{1/2}+\cdots+n^{1/n})/n$
positive_passages.docid: 7510
positive_passages.text: Methods to find $\lim\limits_{n\to\infty}\frac1n\sum\limits_{k=1}^nn^{1/k} $
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: 84384
negative_passages.text: Evaluate $\lim_{n\to \infty}\left(\frac{1}{\sqrt{n(n+1)}}+\frac{1}{\sqrt{(n+1)(n+2)}}+\cdots+\frac{1}{\sqrt{(2n-1)2n}}\right)$
negative_passages.docid: 20843
negative_passages.text: Evaluate the limit of $\lim_{n\to\infty}\frac{1}{n^2}\left(\frac{2}{1}+\frac{9}{2}+\frac{64}{9}+\cdots+\frac{(n+1)^{n}}{n^{n-1}}\right)$
negative_passages.docid: 156557
negative_passages.text: How to compute $\lim_{n\rightarrow\infty}e^{-n}\left(1+n+\frac{n^2}{2!}\cdots+\frac{n^n}{n!}\right)$
negative_passages.docid: 113336
negative_passages.text: Limit of $(\frac{1}{n^2})^{(\frac{1}{n})}$
negative_passages.docid: 93095
negative_passages.text: Find $\lim\limits_{n \to \infty}\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\cdots\left(1-\frac{1}{n^2}\right)$
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: 5072
negative_passages.text: To evaluate limit of sequence $\left(\left( 1 + \frac1n \right) \left( 1 + \frac2n \right)\cdots\left( 1 + \frac nn \right) \right)^{1/n}$
negative_passages.docid: 156478
negative_passages.text: Prove that $\lim_{n\rightarrow\infty}\frac{x_1^2+x_2^2+\cdots+x_n^2}{n^2}=0$
negative_passages.docid: 19898
negative_passages.text: Limit $\lim (1+(a^{1/n}-1) / b)^n$
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: 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: 98941
negative_passages.text: Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?
negative_passages.docid: 62576
negative_passages.text: How to find $\lim_{n\to\infty}\frac{1!+2!+\cdots+n!}{n!}$?
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: 155638
negative_passages.text: Can't we compute $\lim_{n \to \infty}\frac{1+ \cdots +n}{n^2}=\lim_{n\to\infty}\frac{1}{n^2}+\cdots +\lim_{n\to\infty}\frac{n}{n^2}=0$?