Is the sequence $x_n$ convergent, where $x_n= a_n - \sqrt{2n}$ and $a_n=a_{n-1}+\frac{1}{a_{n-1}}$
22077
Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$
26316
Convergence of $a_n= \frac{n!}{n^n}$?
67303
If $\sum_{n=2}^{\infty} a_n$ is convergent, is $\sum_{n=2}^{\infty}{\sqrt{a_n} \over \ln{n}}\left( n^{a_n}-1 \right)$ convergent as well?
27284
Show that the sequence $\sqrt{2}, \ \sqrt{2+\sqrt{2}}, \ \sqrt{2+\sqrt{2+\sqrt{2+}}}...$ converges and find its limit.
132358
Is the sequence $a_{n+1}=a_n-\frac{1}{a_n}$, $a_0=2$ bounded?
55464
Convergence of sequence given by $x_1=1$ and $x_{n+1}=x_n+\sqrt{x_n^2+1}$
95515
Is $x_{n+1}=\cos x_n$ convergent?
145863
sequence of positive numbers satisfying $a_{n+1}=\frac{2}{a_n+a_{n-1}}$, prove it converges
125925
Convergence of $f_n(x)=x^n(1-x)^n$
69989
Do the following series converge if $a_n>0$ and $ \sum_{n=1}^{\infty}a_n$ diverges?
110680
Convergence of recursive sequence $a_{n+1} =\frac{ 1}{k} \left(a_{n} + \frac{k}{a_{n}}\right)$
140220
Convergence of $\sum_{n=2}^{\infty}\frac{\sqrt{a_{n}}}{\ln\, n}(n^{a_{n}}-1)$
19225
Let $\{a_n\}$ be defined as follows: $a_1 = 2$, $a_{n+1}=\frac{1}{3-a_n}$, if $n \geq 1$. Does $\{a_n\}$ converge?
128260
If $\sum a_n$ converges, so does $\sum a_n^{\frac{n}{n+1}}$
17201
$y_{2n}, y_{2n+1}$ and $y_{3n}$ all converge. What can we say about the sequence $ y_n$?
54659
How prove that $(a_{n})_{n \in \mathbb{N}}$ is convergent with $a_{0}=1$, $a_{n+1}= \sqrt{2a_{n}}$?
107399
A sequence and convergence