query: Convergence and limit of a recursive sequence $x_{n+1}=\sqrt{p+x_n}$
positive_passages.docid: 686
positive_passages.text: $\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
negative_passages.docid: 40797
negative_passages.text: $(a_n+a_{n+1})$ is convergent implies $(a_n/n)$ converges to $0$
negative_passages.docid: 85268
negative_passages.text: Convergence of $\sum_{n=1}^{\infty}{\sqrt[n]{n}-1 \over n}$
negative_passages.docid: 86965
negative_passages.text: Limit of this recursive sequence: $x_{n+1}=\bigl(1-\frac{1}{2n}\bigr)x_{n}+\frac{1}{2n}x_{n-1}.$
negative_passages.docid: 151593
negative_passages.text: Prove that the limit of $\sqrt{n+1}-\sqrt{n}$ is zero
negative_passages.docid: 119145
negative_passages.text: $\lim\limits_{n\rightarrow\infty} \sqrt{n}(\sqrt{n+1}-\sqrt{n})$
negative_passages.docid: 98167
negative_passages.text: If a sequence $(u_n)$ be such that its every subsequence has a subsequence that converges to $0$, then $\lim u_n= 0$
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: 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: 88365
negative_passages.text: Prove the sequence converge and find its limit
negative_passages.docid: 149806
negative_passages.text: Is it possible to utilize the convergence of the sequence $z_{n+1}=a/(1+z_n)$ to prove that the sequence $x_{n+2} = \sqrt{x_{n+1} x_n}$ is convergent?
negative_passages.docid: 128181
negative_passages.text: Find $\lim_{n\to\infty}{\sqrt{n+1}-\sqrt{n}}$ with basic methods
negative_passages.docid: 5797
negative_passages.text: Limit of the sequence $a_n=\sqrt[n+1]{(n+1)!}-\sqrt[n]{n!}$
negative_passages.docid: 15319
negative_passages.text: Convergence of recurrence sequence
negative_passages.docid: 79266
negative_passages.text: Proving a sequence defined by a recurrence relation converges
negative_passages.docid: 29266
negative_passages.text: Limit of a sequence defined by recursive relation : $ a_n = \sqrt{a_{n-1}a_{n-2}}$
negative_passages.docid: 60024
negative_passages.text: Proof that a sequence is convergent