query: $\lim\limits_{n \rightarrow \infty} \sqrt{n^2+n} -n$?
positive_passages.docid: 13148
positive_passages.text: Limits: How to evaluate $\lim\limits_{x\rightarrow \infty}\sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$
negative_passages.docid: 41434
negative_passages.text: Show that: $\lim \limits_{n \rightarrow+\infty} \int_{0}^{1}{f(x^n)dx}=f(0)$
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: 17534
negative_passages.text: Find $\lim_{n\to \infty}({1\over \sqrt{n^2+1}}+{1\over \sqrt{n^2+2}}+\cdots+{1\over \sqrt{n^2+n}})$
negative_passages.docid: 98367
negative_passages.text: Limit of $\left(\frac{n^2+2}{2n^2+1}\right)^{n^2}$
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: 156141
negative_passages.text: Limit of $\left(1-\frac{1}{n^2}\right)^n$
negative_passages.docid: 123970
negative_passages.text: Find $L=\lim \limits_{n\to \infty}\sqrt[n]{x^n+y^n+z^n}$
negative_passages.docid: 105064
negative_passages.text: What is wrong with this fake proof that $\lim\limits_{n\rightarrow \infty}\sqrt[n]{n!} = 1$?
negative_passages.docid: 42241
negative_passages.text: Evaluation of $\lim_{n\rightarrow \infty}\sum^{n}_{r=1}\frac{r}{n^2+n+r}$
negative_passages.docid: 8773
negative_passages.text: Finding $\lim\limits_{n \to \infty}{\frac{1^1+2^2+3^3+\cdots+n^n}{n^n}}$
negative_passages.docid: 104996
negative_passages.text: Limit of $\lim_{n\rightarrow \infty} \sum^{n}_{i=1} \frac{1}{\sqrt {n^2 +i} }$
negative_passages.docid: 18353
negative_passages.text: Evaluate of $\lim_{n\rightarrow \infty}\left(\frac{n+1}{n}\right)^{n^2}\cdot \frac{1}{e^n}$
negative_passages.docid: 90773
negative_passages.text: $\lim_{n\rightarrow\infty}\frac{1}{n}\sum_{k=1}^{n}\frac{k}{k^{2}+1}$
negative_passages.docid: 4003
negative_passages.text: Limit of : $\lim\limits_{n\to\infty}{(\sqrt[3]{n+1}-\sqrt[3]{n})}$.
negative_passages.docid: 37394
negative_passages.text: How to find $\lim\limits_{n\to\infty} n·(\sqrt[n]{a}-1)$?
negative_passages.docid: 37755
negative_passages.text: Limit $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}$