Beef with solution to showing sequence $\{s_n\}$ converges where $s_{n+1} = \sqrt{2 + \sqrt{s_n}}$
69717
Find limit of recursive sequence $a_{n+1} =\sqrt{2+ \sqrt{a_n} }.$
62127
Prove recursively defined sequence converges
20136
Convergence of the sequence $ \sqrt {n-2\sqrt n} - \sqrt n $
9789
Convergence of a sequence of non-negative real numbers $x_n$ given that $x_{n+1} \leq x_n + 1/n^2$.
112430
Prove that sequence $ x_{(n+1)}= \frac {a}{1+x_n}$ is convergent to positive root of $x^2+x-a=0,$where $a >0$ and $x_1 >0$
79266
Proving a sequence defined by a recurrence relation converges
74522
Convergence of a sequence, $a_n=\sum_1^nn/(n^2+k)$
49507
Is this sequence convergent?
16970
Convergence of $\sqrt{n}x_{n}$ where $x_{n+1} = \sin(x_{n})$
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 $\lim_{x \to \infty} \{a_n\}$
17902
Prove or disprove: $\sum a_n$ convergent, where $a_n=2\sqrt{n}-\sqrt{n-1}-\sqrt{n+1}$.
17231
How I can prove that the sequence $\sqrt{2} , \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}$ converges to 2?
46685
Show that the sequence $a_1=1$, $a_2=2$, $a_{n+2} = (a_{n+1}+a_n)/2$ converges by showing it is Cauchy
144786
Show that the following inductively defined sequence converges and find its limit.
85268
Convergence of $\sum_{n=1}^{\infty}{\sqrt[n]{n}-1 \over n}$
80683
Convergence of $\sum_{n=1}^\infty\frac{1}{n} [1+\frac{1}{\sqrt{2}}+.....+\frac{1}{\sqrt{n}}]$
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$