CMR với mọi số tự nhiên lớn hơn 2 thì :

\(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2^n-1}>\dfrac{n}{2}\)

Cho a,b,c \(\ge0,a+b+c=1\)

CMR:

ab+ac+bc\(\ge8\left(a^2+b^2+c^2\right)\left(a^2b^2+b^2c^2+c^2a^2\right)\)

Cho x\(\ge0\). CMR:

\(\dfrac{2\sqrt{2}}{\sqrt{x+1}}+\sqrt{x}\le\sqrt{x+9}\)

Cho a,b,c \(\ge0\)

Cmr: \(a^2\left(b+c-a\right)+b^2\left(c+a-b\right)+c^2\left(a+b-c\right)\le3abc\)

Cho a,b,c>0  CMR : 

\(\dfrac{ab}{a+b}+\dfrac{bc}{b+c}+\dfrac{ac}{a+c}\le\dfrac{a+b+c}{2}\)