query: Limit of the Recursive Sequence $X_1=1, X_{n+1}= \frac 1{1 + X_n}$
positive_passages.docid: 24019
positive_passages.text: Solving Recurrence Relation Denominator
negative_passages.docid: 47922
negative_passages.text: Prove that the sequence $(a_n)$ defined by $a_0 = 1$, $a_{n+1} = 1 + \frac 1{a_n}$ is convergent in $\mathbb{R}$
negative_passages.docid: 123253
negative_passages.text: Limit of a sequence $a_1=1;a_{n+1}=(n+1)(1+a_n)$
negative_passages.docid: 39488
negative_passages.text: Limit of a sequence involving root of a factorial: $\lim_{n \to \infty} \frac{n}{ \sqrt [n]{n!}}$
negative_passages.docid: 141463
negative_passages.text: Convergence of $x_{n+1} = \frac12(x_n + \frac2{x_n}).$
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: 108929
negative_passages.text: Proving the limit of a function of a sequence is equal to the function of the limit of that sequence
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: 33976
negative_passages.text: Prove that $\lim_{n \to \infty} \sqrt[n]{a} = 1$ using only the basic properties of sequences
negative_passages.docid: 97747
negative_passages.text: Limit of $\lim\limits_{n\to\infty} (1 + \frac{x_n}{n})^n$
negative_passages.docid: 74286
negative_passages.text: Prove: $\lim_{n\to\infty} \frac{\sum^n_{k=1} \frac{1}{k}}{ \ln(n) } = 1$
negative_passages.docid: 142778
negative_passages.text: Finding $\lim_{n\to\infty}a_n$ if $a_0=a,a_1=b$ and $a_n=\frac{1}{2}(a_{n-1}+a_{n-2})$ where $a, b \in \mathbb{R}$
negative_passages.docid: 34723
negative_passages.text: Proof of a limit for a recursively-defined sequence
negative_passages.docid: 93022
negative_passages.text: Prove that a given recursion sequence converges
negative_passages.docid: 89263
negative_passages.text: Find the limit $\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k+n}$
negative_passages.docid: 97047
negative_passages.text: Limit for sequence $a_{m+n}\leq a_m+a_n$
negative_passages.docid: 51231
negative_passages.text: Find the limit of $\frac{n^{x}}{(1 + x)^{n}}$