The inequality $\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{x+y}\ge \frac{3}{2}$
15116
Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$
52204
Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$
66707
How to prove this inequality? $ | z-1 | \le | | z | -1 | + | z| \cdot | \arg z | $
112676
Inequality $(a+b+c)(ab+bc+ca)(a^3+b^3+c^3)\le (a^2+b^2+c^2)^3$
104272
Inequality of $\vert \text{tanh}(x)-x+\frac{x^3}{3}\vert\leq\frac{1}{8}$ for $x\in[-1/4,1/4]$
92692
Prove $3(x^2y+y^2z+z^2x)(xy^2+yz^2+zx^2)\ge xyz(x+y+z)^3$
18399
Prove this inequality $\sum \cos{A}\ge\frac{1}{4}(3+\sum\cos{(A-B)})$
40700
Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$
103851
Show that $\frac{xy}{z} + \frac{xz}{y} + \frac{yz}{x} \geq x+y+z $ by considering homogeneity
7404
Induction and convergence of an inequality: $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\leq \frac{1}{\sqrt{2n+1}}$
1305
Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$
111847
For $a,b,c>0$, prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c+\frac{4(a-b)^2}{a+b+c}$
157416
Prove inequality: $\sum \frac{a^4}{a^3+b^3} \ge \frac{a+b+c}{2}$
149700
Prove that $\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \cdots \frac{a_n^2}{a_n+a_1} \geq \frac12$
124654
Prove this inequality: $\frac n2 \le \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac1{2^n - 1} \le n$
126557
Proving the inequality $\sum_{\text{cyc}} \frac{a}{a^2+b^3+c^3}\le\frac1{5abc}$
28499
Inequality.$\sqrt{\frac{2a}{b+c}}+\sqrt{\frac{2b}{c+a}}+\sqrt{\frac{2c}{a+b}} \leq 3$