$ \vert x_m - x_n\vert \le \frac{K^{n-1}}{1-K}\vert x_2-x_1\vert $
43907
Contraction mapping in the context of $f(x_n)=x_{n+1}$.
136652
Closed form expression for the product $\prod\limits_{k=1}^{n}\left(1 - \frac{1}{ak}\right)$
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
13902
Show that $\frac{1}{x_1^2}+\frac{1}{4\cdot x_2^2}+\ldots+\frac{1}{n^2\cdot x_n^2}\leq\frac{3n-2}{2n-1}$.
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
94558
Show that $\phi(mn) = \phi(m)\phi(n)\frac{d}{\phi(d)}$
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
42976
How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
107258
Proving If $k \le \left\lfloor \frac{n}{2} \right\rfloor$ then $\binom{n}{k-1} < \binom{n}{k}$
63104
Dual cone of $K = \{(x,t) \mid \| \boldsymbol{x} \|_1 \le t \}$
12781
Prove the following inequality $\sqrt[n]{x_1x_2...x_n}\ge (n-1)$
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
95095
$x_{n+m}\le \frac{x_n+x_{n+1}+\cdots+x_{n+m-1}}{m}$. Prove that this sequence has a limit.
10902
Showing that $ \prod\limits_{i=0}^{n} {n \choose i}\leq(\frac{2^n-2}{n-1})^{n-1} $
78471
Closure of $\{\frac{1}{n}\}:=M$
151805
Prove that $\tau (x_1 x_2 ... x_k) \tau^{-1} = (\tau(x_1) \tau(x_2) ... \tau (x_k))$