Prove convergence of sequence defined recursively $a_{n+1} = \sqrt{6+a_n}$
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
110680
Convergence of recursive sequence $a_{n+1} =\frac{ 1}{k} \left(a_{n} + \frac{k}{a_{n}}\right)$
17231
How I can prove that the sequence $\sqrt{2} , \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}$ converges to 2?
142
Showing the sequence converges to the square root
12031
Asymptotic behavior of the sequence $a_n=\sqrt{n+a_{n-1}}$
88365
Prove the sequence converge and find its limit
89325
$a_{m+n}\leq a_ma_n$ implies the convergence of $\sqrt[n]a_n$
104344
Prove if $|a_{n+1}|/|a_n| \leq |b_{n+1}|/|{b_n}|$ and $\sum |b_n|$ is convergent, then $\sum |a_n|$ is convergent
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?
61212
Using BMCT to prove the sequence $a_{n+1} = \sqrt{2 + a_n}$ is bounded and increasing.
153736
Question about convergence of a simple recursive sequence
74522
Convergence of a sequence, $a_n=\sum_1^nn/(n^2+k)$
13701
Prove convergence of the sequence $(z_1+z_2+\cdots + z_n)/n$ of Cesaro means
155695
The convergence of a sequence
93545
Showing the sequence converges $a_{1}=\frac{1}{2}$, $a_{n+1}=\frac{1}{2+a_{n}}$
132140
Convergence of Sequence of Real Numbers
29266
Limit of a sequence defined by recursive relation : $ a_n = \sqrt{a_{n-1}a_{n-2}}$