Let a sequence ${[a_n]}$ be defined such that $a_1=1$ and when $n\ge1$, $a_{n+1}=a_n+\frac{1}{a_n}$. Then, show that:$12<a_{75}<15$
58187
Solve the sequences inequality
145863
sequence of positive numbers satisfying $a_{n+1}=\frac{2}{a_n+a_{n-1}}$, prove it converges
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.
99782
$a_{n+1}=|a_n|-a_{n-1} \implies a_n \; \text{is periodic}$
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?
132947
How to calculate the limit of $\frac{a_n}{n^2}$ for the sequence $a_{n+1}=a_n+\frac{2 a_{n-1}}{n+1}$?
84900
Concerning the sequence $\Big(\dfrac {\tan n}{n}\Big) $
112663
Let $a_n$ be a sequence s.t $a_1 > 0 \land a_{n+1} = a_n + \dfrac{1}{a_n}$. Prove that $a_n$ is increasing and tends to infinity
110680
Convergence of recursive sequence $a_{n+1} =\frac{ 1}{k} \left(a_{n} + \frac{k}{a_{n}}\right)$
41445
Show that the sequence $a_n\leq a_{2n}+a_{2n+1}$ diverges
53001
If $|f'(c)| \leq M$ and $ M < 1$, the sequence defined by $a_{n+1} = f(a_n)$ converges
34723
Proof of a limit for a recursively-defined sequence
153121
show that $\{x_n\}$ is a cauchy sequence
14836
A polynomial sequence
93545
Showing the sequence converges $a_{1}=\frac{1}{2}$, $a_{n+1}=\frac{1}{2+a_{n}}$
50087
Convergence of $a_{n+1}=\frac{1}{1+a_n}$
100580
Proof that a sequence converges.