Discuss the convergence of the sequence: $a_1=1,a_{n+1}=\sqrt{2+a_n} \quad \forall n \in \mathbb{N}$
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
20136
Convergence of the sequence $ \sqrt {n-2\sqrt n} - \sqrt n $
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?
40797
$(a_n+a_{n+1})$ is convergent implies $(a_n/n)$ converges to $0$
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 $x_1 >0$
41836
If $\sum a_n$ converges, then $\sum \sqrt{a_na_{n+1}}$ converges
141463
Convergence of $x_{n+1} = \frac12(x_n + \frac2{x_n}).$
65592
Convergence of $a_n=(1/2)^{(1/3)^{...^{(1/n)}}}$
29266
Limit of a sequence defined by recursive relation : $ a_n = \sqrt{a_{n-1}a_{n-2}}$
132358
Is the sequence $a_{n+1}=a_n-\frac{1}{a_n}$, $a_0=2$ bounded?
38002
how to prove that this positive sequence converges to 1
107399
A sequence and convergence
142509
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.
80683
Convergence of $\sum_{n=1}^\infty\frac{1}{n} [1+\frac{1}{\sqrt{2}}+.....+\frac{1}{\sqrt{n}}]$
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
78886
Convergence of the sequence $\sqrt{1+2\sqrt{1}},\sqrt{1+2\sqrt{1+3\sqrt{1}}},\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1}}}},\cdots$
50087
Convergence of $a_{n+1}=\frac{1}{1+a_n}$