Let $x_0=0$. Define $x_{n+1}=\cos x_n$ for every $n\ge 0$
68518
What does recursive cosine sequence converge to?
122213
Proving that if $\langle Ax,x\rangle =0$ for every $x$, then $A$ is the zero operator
67214
Function $ y = x^n - nx$, where $x \geq 0$ and $n \geq 2$.
43907
Contraction mapping in the context of $f(x_n)=x_{n+1}$.
40797
$(a_n+a_{n+1})$ is convergent implies $(a_n/n)$ converges to $0$
68484
Revision of Borel-Cantelli, $(X_n)_{n \geq 1}$ sqn of $\geq 0$ identical RVs with $E(X) < \infty$ then $X_n/n \to 0$ a.s., are my arguments correct?
55266
Prove that $(n+1)^{n-1}<n^n$
99782
$a_{n+1}=|a_n|-a_{n-1} \implies a_n \; \text{is periodic}$
54427
$\left|x_{n+1} - x_n\right| < C\left|x_n - x_{n-1}\right|$ prove this is Cauchy
72377
Show that $\sum_{n=1}^\infty r^n\cos(n\theta)=\dfrac{r\cos\theta -r^2}{1-2r\cos\theta+r^2}$ whenever $0<r<1$.
149716
Prove that $ \sqrt{n(n+1)(n+2)(n+3)+1} $ is always a natural number
49233
Find $cot\space x_n$ if $sin(x_{n+1}-x_n)+2^{-(n+1)}sin\space x_nsin \space x_{n+1}=0$ for $n\ge1$
83337
If $A ∈M_n(C)$ is such that $(Ax,x) = 0$ for all $x ∈C^n$, then $A = 0$
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
83638
Suppose $0,0,1,0,0,1,0,0,1,...$ is a sequence. What is the general term of this sequence?
150088
Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$
122914
An integer $n$, such that $nx = 0$, where $x$ belongs to the quotient group $\Bbb Q/\Bbb Z$