Has it yet been proven that $x_{n+1}=x_n-\frac{1}{x_{n}}$ with $x_0=2$ is unbounded?
132358
Is the sequence $a_{n+1}=a_n-\frac{1}{a_n}$, $a_0=2$ bounded?
79767
Properties of $x_k=\frac{a_{k+1}-a_{k}}{a_{k+1}}$ where $\{a_n\}$ is unbounded, strictly increasing sequence of positive reals
38185
Prove that $\{\cos(nx) : n=1, ... ,\infty \}$ is bounded but not totally bounded in $C([0,\pi])$
146528
Define $I_n=\int_0^1\frac{x^n}{\sqrt{x^2+1}}dx$ for every $n\in\mathbb{N}$. Prove that $\lim_{n\to\infty}nI_n=\frac{1}{\sqrt 2}$.
59911
Looking for help with a proof that n-th derivative of $e^\frac{-1}{x^2} = 0$ for $x=0$.
9781
How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
114315
The sequence 1/(n-1) is apparently unbounded yet convergent. What am I missing here?
31174
Find the limit if it exists of $S_{n+1} = \frac{1}{2}(S_n +\frac{A}{S_n})$
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
107842
Behaviour of ($\overline{a}_n)_{n=1}^{\infty}$ and ($\underline{a}_n)_{n=1}^{\infty}$
149806
Is it possible to utilize the convergence of the sequence $z_{n+1}=a/(1+z_n)$ to prove that the sequence $x_{n+2} = \sqrt{x_{n+1} x_n}$ is convergent?
73812
Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
88782
Finding the limit of $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$
34025
Limit of the Sequence: $a_{n+1}=a_n+\frac{1}{a_n}$ with $a_1=1$
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?
33495
A limit problem about $a_{n+1}=a_n+\frac{n}{a_n}$