Prove that $x+\frac{1}{x}\geq2$
44233
How to prove this inequality $ x + \frac{1}{x} \geq 2 $
87411
Prove that $\sqrt{x_1}+\sqrt{x_2}+\cdots+\sqrt{x_n} \geq (n-1) \left (\frac{1}{\sqrt{x_1}}+\frac{1}{\sqrt{x_2}}+\cdots+\frac{1}{\sqrt{x_n}} \right )$
90902
Prove $\frac{a+b+c}{abc} \leq \frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2}$.
3110
Prove $\frac{1}{\sqrt{x}}\geq \frac{\ln x}{x-1}$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
12020
Prove $\sqrt{n+1}-\sqrt{n}\lt \frac{1}{2\sqrt{n}}$
110153
How to prove this inequality?$\frac{1}{n+1} + \frac{1}{n+2} + \cdots+\frac{1}{n+n} + \frac{1}{4n} > \ln 2$
13902
Show that $\frac{1}{x_1^2}+\frac{1}{4\cdot x_2^2}+\ldots+\frac{1}{n^2\cdot x_n^2}\leq\frac{3n-2}{2n-1}$.
15205
Proving that the series 1 + ... + $1 / \sqrt{x}$ < $2 \sqrt{x}$
146594
Prove that $\frac{d}{dx}(\tan^{-1}(x))=\frac{1}{1+x^2}dx$
24469
Prove $ 2<(1+\frac{1}{n})^{n}$
5927
How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
105641
Prove that $ab\leq\frac{1}{2\varepsilon}a^2+\frac{\varepsilon}{2}b^2$
30385
Proving that $\frac{e^x + e^{-x}}2 \le e^{x^2/2}$
51653
Prove that $m+\frac{4}{m^2}\geq3$ for every $m > 0$