Prove that $x_1x_2\cdots x_n \geq (n-1)^n$
12781
Prove the following inequality $\sqrt[n]{x_1x_2...x_n}\ge (n-1)$
110153
How to prove this inequality?$\frac{1}{n+1} + \frac{1}{n+2} + \cdots+\frac{1}{n+n} + \frac{1}{4n} > \ln 2$
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
117680
Prove that $|e^{i\theta_1}-e^{i\theta_2}| \leq |\theta_1 - \theta_2|$
117320
Why is this true: $\|x\|_1 \le \sqrt n \cdot \|x\|_2$?
115459
Proving this $F_{n+1} \cdot F_{n-1} - F^2_n = (-1)^n$ by induction
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
108704
Help with proof of $|x+y| \geq |x|-|y|$
107774
Prove $\|x\|_1\le \sqrt n \|x\|_2$
55266
Prove that $(n+1)^{n-1}<n^n$
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
146546
Proving for all integer $n \ge 2$, $\sqrt n < \frac{1}{\sqrt 1} + \frac{1}{\sqrt 2}+\frac{1}{\sqrt 3}+\cdots+\frac{1}{\sqrt n}$
148582
Proof: $\|X\|_2\leq \sqrt{n}\|X\|_\infty$
13902
Show that $\frac{1}{x_1^2}+\frac{1}{4\cdot x_2^2}+\ldots+\frac{1}{n^2\cdot x_n^2}\leq\frac{3n-2}{2n-1}$.
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
725
proof of $\sum_{n=1}^\infty n \cdot x^n= \frac{x}{(x-1)^2}$
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$