How to prove this inequality $\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b} \ge 1.5$?
15116
Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
89128
Proof of Nesbitt's Inequality: $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\ge \frac{3}{2}$?
119668
How prove this inequality: $\sum_{i,j=1}^{n}|x_{i}+x_{j}|\ge n\sum_{i=1}^{n}|x_{i}|$?
49707
Olympiad inequality $\frac{a}{2a + b} + \frac{b}{2b + c} + \frac{c}{2c + a} \leq 1$.
126557
Proving the inequality $\sum_{\text{cyc}} \frac{a}{a^2+b^3+c^3}\le\frac1{5abc}$
73892
Prove $Σ_{cyc}\frac{1}{\left(a+1\right)^2}+\frac{1}{a+b+c+1}\ge 1$
257
Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$
145783
How can I prove this inequality in a triangle: $\frac{1}{(b+c-a)} +\frac{1}{(c+a-b)} +\frac{1}{(a+b-c)} \gt \frac{1}{a} +\frac{1}{b} +\frac{1}{c}$?
98454
Prove that, $\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}\ge 4$ where we do not use AM-GM inequality on the given statement to prove it.
137864
Prove that $ \left(1+\frac a b \right) \left(1+\frac b c \right)\left(1+\frac c a \right) \geq 2\left(1+ \frac{a+b+c}{\sqrt[3]{abc}}\right)$.
110153
How to prove this inequality?$\frac{1}{n+1} + \frac{1}{n+2} + \cdots+\frac{1}{n+n} + \frac{1}{4n} > \ln 2$
7404
Induction and convergence of an inequality: $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\leq \frac{1}{\sqrt{2n+1}}$
108782
Inequality $\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1} \ge 1$
157416
Prove inequality: $\sum \frac{a^4}{a^3+b^3} \ge \frac{a+b+c}{2}$
155341
Proving or disproving inequality $ \frac{xy}{z} + \frac{yz}{x} + \frac{zx}{y} \ge x + y + z $
64277
How to prove ${{a}^{a}}{{b}^{b}}\ge {{\left(\frac{a+b}{2}\right)}^{a+b}}$ ?thanks.