query: Evaluate $\lim_{n \rightarrow \infty}n^2((1 + \frac{1}{n+1})^{n+1} - (1 + \frac{1}{n})^n)$
positive_passages.docid: 40227
positive_passages.text: Compute $\lim\limits_{n\to\infty}n^2\left(\left(1+\frac1{n+1}\right)^{n+1}-\left(1+\frac1n\right)^n\right)$
negative_passages.docid: 154506
negative_passages.text: Evaluating $\lim_{n\rightarrow\infty} (\frac{(1+\frac{1}{n})^n}{e})^n$
negative_passages.docid: 63023
negative_passages.text: Evaluation of $\lim_{x\rightarrow \infty}\sqrt{x^2+x+1} -\lfloor \sqrt{x^2+x+1 }\rfloor\;,$
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: 53537
negative_passages.text: Evaluate $\lim_{n\rightarrow\infty}\sum_{k=1}^n\arcsin(\frac k{n^2})$
negative_passages.docid: 115819
negative_passages.text: Evaluate $\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n})$
negative_passages.docid: 72842
negative_passages.text: Evaluation of the limit $\lim\limits_{n \to \infty } \frac1{\sqrt n}\left(1 + \frac1{\sqrt 2 }+\frac1{\sqrt 3 }+\cdots+\frac1{\sqrt n } \right)$
negative_passages.docid: 74204
negative_passages.text: Evaluate $\lim_{n\to\infty}(1+x)(1+x^2)\cdots(1+x^{2n}),|x|<1$
negative_passages.docid: 56961
negative_passages.text: Evaluate the limit of $\sum_{n=1}^{\infty}\frac{n^2}{n!}$
negative_passages.docid: 82831
negative_passages.text: Evaluating the limit $\lim_{n\to\infty} \left[ \frac{n}{n^2+1}+ \frac{n}{n^2+2^2} + \ldots + \frac{n}{n^2+n^2} \right]$
negative_passages.docid: 9541
negative_passages.text: Evaluate $\lim_{n\to\infty}\frac {qn+1}{qn} \frac {qn+p+1}{qn+p} \cdots \frac {qn+np+1}{qn+np}$ where $p\in\mathbb{N}\setminus\{0,1\},q>0.$
negative_passages.docid: 56902
negative_passages.text: Evaluate $\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$
negative_passages.docid: 94466
negative_passages.text: evaluating the limit $ \lim_{(x,y) \rightarrow (0,0) } \frac{x^2y^2}{x^2 + y^2} $
negative_passages.docid: 113537
negative_passages.text: Limit $\lim_{n\to\infty}\left(1-\frac{1}{3}\right)^2\left(1-\frac{1}{6}\right)^2\cdots\left(1-\frac{1}{\frac{n(n+1)}{2}}\right)^2$
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: 90773
negative_passages.text: $\lim_{n\rightarrow\infty}\frac{1}{n}\sum_{k=1}^{n}\frac{k}{k^{2}+1}$
negative_passages.docid: 17438
negative_passages.text: Evaluate $\lim_{n\to \infty} \sum_{r=1}^n \frac {1}{2^r}\tan \left(\frac {1}{2^r}\right)$