query: Finding the limit of the sequence $x(n) = (1+2/n)^n$
positive_passages.docid: 23217
positive_passages.text: About $\lim \left(1+\frac {x}{n}\right)^n$
negative_passages.docid: 121606
negative_passages.text: How do I prove that the limit of the sequence exists: $a_n = \frac1n +\frac 1{n+1} + \frac1{n+2} + \dots + \frac1{2n}$?
negative_passages.docid: 7389
negative_passages.text: Finding the limit of $\frac{Q(n)}{P(n)}$ where $Q,P$ are polynomials
negative_passages.docid: 128181
negative_passages.text: Find $\lim_{n\to\infty}{\sqrt{n+1}-\sqrt{n}}$ with basic methods
negative_passages.docid: 71391
negative_passages.text: Find the limit of given sequence
negative_passages.docid: 95095
negative_passages.text: $x_{n+m}\le \frac{x_n+x_{n+1}+\cdots+x_{n+m-1}}{m}$. Prove that this sequence has a limit.
negative_passages.docid: 12914
negative_passages.text: What's the limit of the sequence $\lim\limits_{n \to\infty} \frac{n!}{n^n}$?
negative_passages.docid: 18244
negative_passages.text: What is the limit of this sequence? How does it relate to the exponential function?
negative_passages.docid: 4024
negative_passages.text: Finding the limit of $\frac {n}{\sqrt[n]{n!}}$
negative_passages.docid: 27284
negative_passages.text: Show that the sequence $\sqrt{2}, \ \sqrt{2+\sqrt{2}}, \ \sqrt{2+\sqrt{2+\sqrt{2+}}}...$ converges and find its limit.
negative_passages.docid: 40870
negative_passages.text: Sequence Limit Problem: If $0 \leq x_{m+n} \leq x_n + x_m$ then limit of $x_n/n$ exists
negative_passages.docid: 6878
negative_passages.text: Prove limit of sequence
negative_passages.docid: 51231
negative_passages.text: Find the limit of $\frac{n^{x}}{(1 + x)^{n}}$
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: 28552
negative_passages.text: Calculate the limit of two interrelated sequences?
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: 31930
negative_passages.text: Given the sequence $(x_n)$ is unbounded, show that there exist a subsequence $(x_{n_k})$ such that $\lim(1/x_n)=0$.