Better proof of inequality $x - (1 + x) \log(1+x) \leq -\frac{x^2}{2(1+x)}$ for $x > 0$
125680
Show that $(1+u) \log (1+u) - u \ge \frac{u^2}{2(1+u/3)} $
41293
Prove the inequalities $|z_1 +z_2| \geq \frac{1}{2}(|z_1|+|z_2|)|\frac {z_1} {|z_1|} +\frac {z_2} {|z_2|}|$
143968
Proving this inequality by mathematical induction
130553
How do I prove the following inequality $\sum_{k=n+1}^{\infty}\frac{1}{k^{2}\log k}\leq\frac{1}{n\log n}$?
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
146885
How prove this inequality $\frac{a-b}{b+c}+\frac{b-c}{c+d}+\frac{c-d}{d+e}+\frac{d-e}{e+a}+\frac{e-a}{a+b}\ge 0$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
118613
Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
117262
Proving a logarithm inequality
131565
Proof by induction of summation inequality: $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\dots+\frac1{2^n}\ge 1+\frac{n}2$
16524
Proof of an inequality by induction: $(1 + x_1)(1 + x_2)...(1 + x_n) \ge 1 + x_1 + x_2 + ... + x_n$
121548
proof of an inequality $ \left( 1+ \frac{x}{p} \right) ^{p}$
15116
Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$
90896
proof of inequality $e^x\le x+e^{x^2}$
104688
How can I prove that $x-{x^2\over2}<\ln(1+x)$
103030
Proving $\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}$ for $x> 0$
34349
Prove that $\frac{1}{1+x_1}+\frac{1}{1+x_2}+\cdots+\frac{1}{1+x_n} \geq \frac{n}{\sqrt[n]{x_1x_2\cdots x_n}+1}$