query: Evaluate limit of $a_n = \bigg( 1 + \frac{2}{n} \bigg)^n$
positive_passages.docid: 23217
positive_passages.text: About $\lim \left(1+\frac {x}{n}\right)^n$
negative_passages.docid: 128938
negative_passages.text: Finding $\lim_{n\to\infty} a_n^n$ where $a_n=\frac{(n!)^2}{(n+k)!(n-k)!}$
negative_passages.docid: 31174
negative_passages.text: Find the limit if it exists of $S_{n+1} = \frac{1}{2}(S_n +\frac{A}{S_n})$
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: 35169
negative_passages.text: Finding the limit of $\left(\frac{n}{n+1}\right)^n$
negative_passages.docid: 27932
negative_passages.text: Show that $\lim\limits_{n\to\infty}\frac{a_1+a_2+\dots+a_n}{n^2}$ exists and is independent of the choice of $a$
negative_passages.docid: 86348
negative_passages.text: Proving $\sum\limits_{k=0}^{n-1} \Bigl[x + \frac{k}{n}\Bigr] = [nx]$
negative_passages.docid: 32996
negative_passages.text: limit: $u_n=\frac{1+2^2+3^3+...+n^n}{n^n}$.
negative_passages.docid: 113336
negative_passages.text: Limit of $(\frac{1}{n^2})^{(\frac{1}{n})}$
negative_passages.docid: 65275
negative_passages.text: Finding $\lim\limits_{x\to1^-}\Bigl(\prod\limits_{n=0}^{\infty}\Bigl(\frac{1+x^{n+1}}{1+x^n}\Bigr)^{x^n}\Bigr)$
negative_passages.docid: 54775
negative_passages.text: Find $\lim_{n \to \infty} n[(1+\frac{1}{n})^n - e]$
negative_passages.docid: 81654
negative_passages.text: Evaluate $\lim_{n\to\infty} [{1\over kn}+{1\over k(n+1)}+{1\over k(n+2)}+\cdots+{1\over k(n+p-k)}]$ where $k<p$
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: 26408
negative_passages.text: Evaluate a limit (probably involving L'Hôpital rule)
negative_passages.docid: 5974
negative_passages.text: Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$
negative_passages.docid: 120336
negative_passages.text: Evaluation of $\lim_{n\rightarrow \infty}\binom{2n}{n}^{\frac{1}{n}}$
negative_passages.docid: 18353
negative_passages.text: Evaluate of $\lim_{n\rightarrow \infty}\left(\frac{n+1}{n}\right)^{n^2}\cdot \frac{1}{e^n}$