Define sequence $s_1 = \sqrt{2}$ and $s_{n+1} = \sqrt{2+s_n}$. Find $\lim_{n \rightarrow \infty} s_n$ and prove this convergence.
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
5797
Limit of the sequence $a_n=\sqrt[n+1]{(n+1)!}-\sqrt[n]{n!}$
86205
Evaluating the limit of a sequence given by recurrence relation $a_1=\sqrt2$, $a_{n+1}=\sqrt{2+a_n}$. Is my solution correct?
85268
Convergence of $\sum_{n=1}^{\infty}{\sqrt[n]{n}-1 \over n}$
47922
Prove that the sequence $(a_n)$ defined by $a_0 = 1$, $a_{n+1} = 1 + \frac 1{a_n}$ is convergent in $\mathbb{R}$
33976
Prove that $\lim_{n \to \infty} \sqrt[n]{a} = 1$ using only the basic properties of sequences
147661
Show that {$x_n$} is a convergent sequence if $d(x_{n+2}, x_{n+1})≤ rd(x_{n+1}, x_n)$
12031
Asymptotic behavior of the sequence $a_n=\sqrt{n+a_{n-1}}$
132140
Convergence of Sequence of Real Numbers
110680
Convergence of recursive sequence $a_{n+1} =\frac{ 1}{k} \left(a_{n} + \frac{k}{a_{n}}\right)$
155695
The convergence of a sequence
60024
Proof that a sequence is convergent
143263
If $\sum a_n$ is a convergent series with $S = \lim s_n$, where $s_n$ is the nth partial sum, then $\lim_{n \to \infty} \frac{s_1+...+s_n}{n} = S$
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 $\lim_{x \to \infty} \{a_n\}$
88365
Prove the sequence converge and find its limit
61696
Prove that $\{x_1=1,\,x_{n+1}=\frac {x_n}2+\frac 1{x_n} \}$ converges when $n \to \infty$
26500
Prove $\sum_{n=1}^{\infty}|a_{n}b_{n}|$ converges if $\sum_{n=1}^{\infty}a_{n}^{2}$ and $\sum_{n=1}^{\infty}b_{n}^{2}$ converge