Concerning the sequence $ x_1=1 ,\space x_{n+1}=x_n+\dfrac{1}{x_n} $
22077
Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$
123253
Limit of a sequence $a_1=1;a_{n+1}=(n+1)(1+a_n)$
43907
Contraction mapping in the context of $f(x_n)=x_{n+1}$.
27217
For the Fibonacci sequence prove that $\sum_{i=1}^n F_i= F_{n+2} - 1$
49621
Proof of "well-founded iff there is no sequence $x_n$ s.t. $(x_{n+1}, x_n) \in R$"
145863
sequence of positive numbers satisfying $a_{n+1}=\frac{2}{a_n+a_{n-1}}$, prove it converges
25294
Monotonicity of the sequences $\left(1+\frac1n\right)^n$, $\left(1-\frac1n\right)^n$ and $\left(1+\frac1n\right)^{n+1}$
110310
$|x_{n+1} - x_n| \le C |x_n - x_{n-1}|.$ Prove $(x_n)$ is cauchy
14836
A polynomial sequence
59584
A sequence of real numbers such that $\lim_{n\to+\infty}|x_n-x_{n+1}|=0$ but it is not Cauchy
19657
Does the recursive sequence $a_1 = 1, a_n = a_{n-1}+\frac{1}{a_{n-1}}$ converge?
25583
Show that the sequence $a_0 = 1$, $a_{n+1 }= \sqrt{2+a_n}$ is monotonically increasing
12031
Asymptotic behavior of the sequence $a_n=\sqrt{n+a_{n-1}}$
95515
Is $x_{n+1}=\cos x_n$ convergent?
141463
Convergence of $x_{n+1} = \frac12(x_n + \frac2{x_n}).$
64885
Irrational and rational sequence proof
9789
Convergence of a sequence of non-negative real numbers $x_n$ given that $x_{n+1} \leq x_n + 1/n^2$.