Prove ${a+b+c\over abc}\leq {1\over a^2}+{1\over b^2}+{1\over c^2}$
90902
Prove $\frac{a+b+c}{abc} \leq \frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2}$.
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$
15116
Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
56101
Prove the inequality $\frac{a}{c+a-b}+\frac{b}{a+b-c}+\frac{c}{b+c-a}\ge{3}$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
3109
Prove that $(p+q)^m \leq p^m+q^m$
104688
How can I prove that $x-{x^2\over2}<\ln(1+x)$
91617
Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
52625
Prove inequality $\sqrt{\frac{2a}{b+a}} + \sqrt{\frac{2b}{c+b}} + \sqrt{\frac{2c}{a+c}} \leq 3$
6621
Prove the inequality $a^2bc+b^2cd+c^2da+d^2ab \leq 4$ with $a+b+c+d=4$
62417
Prove This Inequality ${\pi \over 2} \le \sum_{n=0}^{\infty} {1 \over {1+n^2}} \le {\pi \over 2} + 1$
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
73987
Prove the inequality $({1+\frac{a}b})^n$ + $(1+\frac{b}a)^n$ $\geq$ $2^{n+1}$
154716
Prove $\frac{1}{a^3+b^3+abc}+\frac{1}{a^3+c^3+abc}+\frac{1}{b^3+c^3+abc} \leq \frac{1}{abc}$