Is $x_{n+1}=\frac{x_n}{2}-\frac{2}{x_n}$ bounded?
3211
The sequence $x_{n+1}=\frac{x_n}{2}-\frac{2}{x_n}, x_0>0$ is bounded?
54513
Prove $\frac 1{x+1}<\ln\left(\frac{x+1}x\right)<0.5\left(\frac 1x+\frac 1{x+1}\right)$
63523
$|a_{n+1}-a_n| \leq \frac{1}{2} |a_{n}-a_{n-1}|$. Prove $(a_n)$ is Cauchy
132948
Prove if $\left\{x_n\right\}$ converges to $2$, then $\left\{\frac{1}{x_n}\right\}$ converges to $\frac{1}{2}$
147021
Proving a function is bounded
113151
Does $\sum\limits_{i=1}^{\infty}|a_i||x_i| < \infty$ whenever $\sum\limits_{i=1}^{\infty} |x_i| < \infty $ imply $(a_i)$ is bounded?
26837
Limit of the sequence $\{n^n/n!\}$, is this sequence bounded, convergent and eventually monotonic?
31174
Find the limit if it exists of $S_{n+1} = \frac{1}{2}(S_n +\frac{A}{S_n})$
131847
$\frac{(x-1)(x+1)}{ (x+1)} \rightarrow (x-1)$ Domain Change
35611
How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$?
153272
Basic question about $\sup_{x\neq 0}{} \frac{\|Ax\|}{\|x\|} = \sup_{\|x\| = 1}{\|Ax\|} $, $x \in\mathbb{R}^n$
85217
Boundedness and convergence of $x_{n+1} = x_n ^2-x_n +1$
118362
Determine whether $f_n(x)=\frac{x^n}{\sqrt{3n}}$ for $x \in [0,1]$ is uniformly convergent
18153
To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$
52324
Tight bound for $T(n) = T(n^{1/2}) + 1$
12020
Prove $\sqrt{n+1}-\sqrt{n}\lt \frac{1}{2\sqrt{n}}$
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$