Finding limit point of recursively defined sequence $a_{n+1}=\sqrt{2+a_n}$.
57095
How do I prove the sequence $x_{n+1}=\sqrt{\alpha +x_n}$, with $x_0=\sqrt \alpha$ converges? ( boundedness?)
115111
Limit of the sequence $nx_{n}$ where $x_{n+1} = \log (1 +x_{n})$
156814
Compute the limit of the sequence ${\textstyle\sum_{k=1}^n}\frac1{\sqrt{n^2+k}}$
128517
A recursive sequence is defined by...
31551
Prob. 3, Chap. 3 in Baby Rudin: If $s_1 = \sqrt{2}$, and $s_{n+1} = \sqrt{2 + \sqrt{s_n}}$, what is the limit of this sequence?
107953
Limit of the sequence $\lim_{n\rightarrow\infty}\sqrt[n]n$
74629
Find the limit of the sequence $\{\frac{x_1 + 2x_2 + ... + nx_n}{n^2}\}$, where $\{x_n\}$ is a convergent sequence in a normed space S.
49860
Determine the convergence of $\sum\limits_{n=2}^\infty \frac{\sqrt{n+1}}{n(n-1)}$
62127
Prove recursively defined sequence converges
68609
Let $a_{n+1}=\sqrt{a_1+a_2+\cdots+a_n}$ .Prove that $ \lim\limits_{n \rightarrow \infty} \frac{a_n}{n}=\frac{1}{2}$
49828
Show that the sequence $\sqrt{2},\sqrt{2\sqrt{2}},\sqrt{2\sqrt{2\sqrt{2}}},...$ converges and find its limit.
18219
(ZF)subsequence convergent to a limit point of a sequence
18675
$\{a_n\}$ sequence $a_1=\sqrt{6}$ for $n \geq 1$ and $a_{n+1}=\sqrt{6+a_n}$ show it that convergence and also find $\lim_{x \to \infty} \{a_n\}$
25583
Show that the sequence $a_0 = 1$, $a_{n+1 }= \sqrt{2+a_n}$ is monotonically increasing
149806
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?
55464
Convergence of sequence given by $x_1=1$ and $x_{n+1}=x_n+\sqrt{x_n^2+1}$
67420
Limit of quotient sequence