query: How can I show following sequence of square root is convergent?
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: 37389
negative_passages.text: Why is this sequence of functions not uniformly convergent?
negative_passages.docid: 19174
negative_passages.text: Definition of convergence of a nested radical $\sqrt{a_1 + \sqrt{a_2 + \sqrt{a_3 + \sqrt{a_4+\cdots}}}}$?
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: 9134
negative_passages.text: Suppose $\sum{a_n}$ converges. How do I prove that $\sum{\frac{\sqrt{a_n}}{n}}$ converges
negative_passages.docid: 15319
negative_passages.text: Convergence of recurrence sequence
negative_passages.docid: 136421
negative_passages.text: How to prove convergence of $\sum\limits_{n=1}^\infty \frac{\sqrt a_n}{n^\alpha}$
negative_passages.docid: 27068
negative_passages.text: Show that $\sqrt{2+\sqrt{2+\sqrt{2...}}}$ converges to 2
negative_passages.docid: 79266
negative_passages.text: Proving a sequence defined by a recurrence relation converges
negative_passages.docid: 93545
negative_passages.text: Showing the sequence converges $a_{1}=\frac{1}{2}$, $a_{n+1}=\frac{1}{2+a_{n}}$
negative_passages.docid: 17231
negative_passages.text: How I can prove that the sequence $\sqrt{2} , \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}$ converges to 2?
negative_passages.docid: 55464
negative_passages.text: Convergence of sequence given by $x_1=1$ and $x_{n+1}=x_n+\sqrt{x_n^2+1}$
negative_passages.docid: 63612
negative_passages.text: Determine convergence of $\sum_{n=1}^{\infty}a_n$
negative_passages.docid: 122413
negative_passages.text: Show $b_n=\sqrt[k]{n+1}-\sqrt[k]{n}$ converges towards $0$ for all $k \geq 2$.
negative_passages.docid: 142509
negative_passages.text: If $\alpha\in (0,1]$ and $x_n=\alpha x_{n-1}+(1-\alpha)x_{n-2}$, show that the sequence $\{x_n\}$ is convergent.
negative_passages.docid: 144786
negative_passages.text: Show that the following inductively defined sequence converges and find its limit.
negative_passages.docid: 141484
negative_passages.text: Convergence of a sequence by convergence of sub-subsequence