Proving $x_{n+1}=\sqrt{\alpha +x_n}, x_0=\sqrt \alpha, \alpha>0$ converges.
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
17902
Prove or disprove: $\sum a_n$ convergent, where $a_n=2\sqrt{n}-\sqrt{n-1}-\sqrt{n+1}$.
85217
Boundedness and convergence of $x_{n+1} = x_n ^2-x_n +1$
54376
Convergence of the series $\sqrt[n]n-1$
143942
Verify proof that sequence converges
9789
Convergence of a sequence of non-negative real numbers $x_n$ given that $x_{n+1} \leq x_n + 1/n^2$.
34904
Proof of Convergence: Babylonian Method $x_{n+1}=\frac{1}{2}(x_n + \frac{a}{x_n})$
47740
Let $x_1=a>0$ and $x_{n+1}=x_n+\frac{1}{x_n} \forall n\in \mathbb N$. Check whether the following sequence converges or diverges.
111353
Show that $\{a_n\}$ defined by $a_{n+1}=\frac{a_n+2}{a_n+1}$ converges
27068
Show that $\sqrt{2+\sqrt{2+\sqrt{2...}}}$ converges to 2
76137
Too simple proof for convergence of $\sum_n a_n b_n$?
7078
If $\sum_n \sqrt{a_n a_{n+1}}$ converges, then $\sum_n a_n$ might not converge.
67638
Show that $x_{n+1}=x_n(2-ax_n)$ converges and find the limit
100234
Proving that $x^n$ converges to $0$ whenever $|x| < 1$
12031
Asymptotic behavior of the sequence $a_n=\sqrt{n+a_{n-1}}$
28587
Show that $\sum\limits_{n=1}^\infty \frac {\sqrt{a_n}}{n}$ converges if $\sum\limits_{n=1}^\infty{a_n}$ does provided that $a_n>0$
25583
Show that the sequence $a_0 = 1$, $a_{n+1 }= \sqrt{2+a_n}$ is monotonically increasing