Prove $\|x\|\le\sum_{i=1}^n|x_i|\le\sqrt{n}\|x\|$ for all $x\in\mathbb{R}^n$.
107774
Prove $\|x\|_1\le \sqrt n \|x\|_2$
62417
Prove This Inequality ${\pi \over 2} \le \sum_{n=0}^{\infty} {1 \over {1+n^2}} \le {\pi \over 2} + 1$
107058
Prove that $E(X\ln X)\le E X E\ln X$
73277
Prove $[\sqrt{x}+\sqrt{x+1}]=[\sqrt{4x+2}], x \in \Bbb N$
124562
$f:\mathbb{R}^n \to \mathbb{R}$ has expansion $\sum_i g_i(x)x^i$
52231
Prove or disprove {$\sum_{i=1}^n x_i^2 = 1$} is convex
139711
prove this inequality with $\sum\limits_\text{cyc}\sqrt{1-xy}\ge 2$
156555
Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$
64336
Show $\sum_{k=1}^n \frac{1}{k^2} \le 2$ and $\ln(n!) \ge 1 -n+n\ln(n)$ for all positive integers n
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
150565
Prove $(a+b)^\frac{1}{n} \le a^\frac{1}{n} + b^\frac{1}{n}$
90896
proof of inequality $e^x\le x+e^{x^2}$
67454
Show that $\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y}) = \sum_{i=1}^n (x_i - \bar{x})(y_i)$.
118613
Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
16253
Proof that $|\sin(nx)| \le n|\sin(x)|$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
111316
PROVE if $x \ge-1 $then $ (1+x)^n \ge 1+nx $ , Every $n \ge 1$