If $a_1= \sqrt{6}$ and $a_{n+1} = \sqrt{6 + a_n}$, what is the limit of $a_n$ as $n$ goes to infinity?
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
11961
Why does $\lim_{n \to\infty}a_{n+1} = \lim_{n\to\infty}a_n$?
33495
A limit problem about $a_{n+1}=a_n+\frac{n}{a_n}$
4003
Limit of : $\lim\limits_{n\to\infty}{(\sqrt[3]{n+1}-\sqrt[3]{n})}$.
99975
Find the Limit (n to infinity)
73696
Given $(a_n)$ with $a_n \geq a_{n+1} \geq 0$ show that if $\sum \sqrt{a_n a_{n+1}} < \infty \implies \sum a_n < \infty$
123576
Why does $\lim_{n\to\infty} z_n=A$ imply $\lim_{n\to\infty}\frac{1}{n}(z_1+\cdots+z_n)=A$?
75571
Limit of $\sqrt x$ as $x$ approaches $0$
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}$
37394
How to find $\lim\limits_{n\to\infty} n·(\sqrt[n]{a}-1)$?
33976
Prove that $\lim_{n \to \infty} \sqrt[n]{a} = 1$ using only the basic properties of sequences
37251
Values of the limit $\lim\limits_{x\to+\infty}\left(\sqrt{(x+a)(x+b)}-x\right)$
128181
Find $\lim_{n\to\infty}{\sqrt{n+1}-\sqrt{n}}$ with basic methods
83318
How to compute the limit $\lim_{n \to \infty} \sqrt[n]{a_1^n + \cdots + a_m^n}$?
46542
How do I calculate $\lim_{x\to+\infty}\sqrt{x+a}-\sqrt{x}$?
69309
How do I simplify and evaluate the limit of $(\sqrt x - 1)/(\sqrt[3] x - 1)$ as $x\to 1$?
68891
Are the limits $\lim\limits_{n\to \infty }\left|\frac{a_{n+1}}{a_n}\right|\,$ and $\lim\limits_{n\to \infty }\sqrt[n]{|a_n|}\,$ equal?