quanvantruong94

1. cho $abc=2, a^3 >72$. cm: $ \dfrac{1}{3} a^2+b^2+c^2>ab+bc+ca.$

2. $CM: \dfrac{1}{1^3}+ \dfrac{1}{2^3}+....+ \dfrac{1}{2010^3} \leq \dfrac{5}{4} $

3. cho a>b>0 CM:
$ \dfrac{1+a+...+a^{2009}}{1+a+...a^{2010}} < \dfrac{1+b+...+b^{2009}}{1+b+...+b^{2010}}$

4.Cm: $S= \dfrac{1}{n+1}+ \dfrac{1}{n+2}+....+ \dfrac{1}{3n+1} \notin N \forall n \in N*.$

5. CM: $ \dfrac{(2n)!}{(n!)^2} \geq \dfrac{4^n}{n+1}$

6.cho$ x^2+y^2=4.CM \sqrt{2x+2y+6} +\sqrt{22-6x-6y} \geq 4\sqrt{2} $

7.cho a,b>0 thỏa $a^4+b^4+a^3+b^3+a^2+b^2+a+b=7.$
$CM:a+b \leq 2.$

8.cho$ -1 \leq a \leq 1 . CM:-1 \leq 6a \sqrt{1-a^2} + 8a^2 \leq 9. $