Prove that $\frac{c}{c+1}< \frac{a}{a+1} + \frac{b}{b+1}$
8207
Can I prove this inequality algebraically?
145909
Prove that $\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+....+\frac{1}{2n}\geq \frac{2}{3}$
41558
Prove that $\frac4{abcd} \geq \frac a b + \frac bc + \frac cd +\frac d a$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
137791
Proving inequality $\sqrt{\frac{2a}{b+c}}+\sqrt{\frac{2b}{c+a}}+\sqrt{\frac{2c}{a+b}} \leq \sqrt{3 \left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right)}$
24469
Prove $ 2<(1+\frac{1}{n})^{n}$
61186
For which $n$ does $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$ imply $\frac{1}{a^n}+\frac{1}{b^n}+\frac{1}{c^n}=\frac{1}{a^n+b^n+c^n}$
157068
Prove that $\left (\frac{1}{a}+1 \right)\left (\frac{1}{b}+1 \right)\left (\frac{1}{c}+1 \right) \geq 64.$
145632
Proving $\frac{1}{\cos^2\alpha}<\frac{\tan\beta-\tan\alpha}{\beta-\alpha}<\frac{1}{\cos^2\beta}$
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
91000
Prove that $\frac{1}{a+1}0$
38448
Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
134535
Inequality $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \geq a + b+ c$ when $abc = 1$
148744
Prove that $(\frac{bc+ac+ab}{a+b+c})^{a+b+c} \ge \sqrt{(bc)^a(ac)^b(ab)^c}$
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
69653
Inequality $\left(a-1+\frac{1}b\right)\left(b-1+\frac{1}c\right)\left(c-1+\frac{1}a\right)\leq1$