Consider the sequence $x_0 =\cos 0$, $x_{n+1} =\cos x_n$, how do I show it converges?
95515
Is $x_{n+1}=\cos x_n$ convergent?
132140
Convergence of Sequence of Real Numbers
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
46830
Prove that the sequence $a_{n+1} =\frac{1}{2}\left(a_{n}+\frac{c}{a_{n}}\right)$ is convergent and find its limit
99933
Determine whether $(x_n)$ converges if $x_1= a , x_{n+1} = x_n+\frac{1}{x_n}$ for $n \in \mathbb{N}$
86970
Let $\{x_n\}$ be a sequence in a metric space such that $\{x_{2n}\}$, $\{x_{2n+1}\}$ and $\{x_{3n}\}$ all convergent. Show that $\{x_{n}\}$ converges
148410
How do I show $f_n(x)=n^2 x^n(1-x)$ pointwise converges to $0$ on $[0,1]$?
35885
Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
106000
Determine if $f_n(x)= \big(\cos (\frac x {\sqrt n} )\big )^n $ converges pointwise or/and uniformly?
142509
If $\alpha\in (0,1]$ and $x_n=\alpha x_{n-1}+(1-\alpha)x_{n-2}$, show that the sequence $\{x_n\}$ is convergent.
33965
Convergence of $\sum_{n=1}^\infty (-1)^n(\sqrt{n+1}-\sqrt n)$
126264
Does the series $\sum \limits _{n=0}^{\infty} \cos(n\pi)$ converge or diverge?
3404
What are the convergent sequences in the cofinite topology
48763
Convergence of $\sum_{n=1}^\infty \frac{\cos(n)}{n}$
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.
141484
Convergence of a sequence by convergence of sub-subsequence
93545
Showing the sequence converges $a_{1}=\frac{1}{2}$, $a_{n+1}=\frac{1}{2+a_{n}}$