Asymptotic behavior of $x_{n+1}=x_n+\frac{1}{x_n}, \space\space\space x_0=1$
22077
Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$
85217
Boundedness and convergence of $x_{n+1} = x_n ^2-x_n +1$
150092
Iterated sums and asymptotics
95095
$x_{n+m}\le \frac{x_n+x_{n+1}+\cdots+x_{n+m-1}}{m}$. Prove that this sequence has a limit.
43829
Limit of $h_n(x)=x^{1+\frac{1}{2n-1}}$
42519
$\lim_{n \rightarrow \infty} \sum^n_{k=1} \frac{1}{k+n}$
193
On Cesàro convergence: If $ x_n \to x $ then $ z_n = \frac{x_1 + \dots +x_n}{n} \to x $
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
63562
Show that $x_{n+1}-\dfrac{x_n}{2}$ converges to zero implies that $(x_n)_n$ also converges to zero.
10408
Uniformly convergence of $f_{n+1}(x)= \int^x_0 f_n(t)dt$
100234
Proving that $x^n$ converges to $0$ whenever $|x| < 1$
31174
Find the limit if it exists of $S_{n+1} = \frac{1}{2}(S_n +\frac{A}{S_n})$
104602
asymptotic of $x^{x^x} = n$
61487
Limit of $\frac1n\sqrt[n]{(n+1)(n+2)(n+3)...(n+n)}$
61731
Prove that for each $n \in \mathbb N$, $\gamma_n=1+\frac{1}{2}+\dots+\frac{1}{n}-\int_1^n \frac{1}{x}dx$ is convergent
70067
Asymptotics of $\max\limits_{1\leqslant k\leqslant n}X_k/n$
112512
How to prove that there are finitely many $n$ such that $f(1+1/n) = \frac{1}{n+1}$?