If a, b, c \in N , and 1\leq a\leq b\leq c , find all a,b,c numbers that hold the equation always true,

\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=\dfrac{3}{4}

If n \in N^+ , prove

\dfrac{1}{2}\leq\dfrac{1}{n+1}+\dfrac{1}{n+2}+\dots+\dfrac{1}{2n}<1

Proof of AM-GM inequality of three terms

\dfrac{a+b+c}{3} \geq \sqrt[3]{abc}

(a, b,c > 0)

Using geometric method to prove AM GM inequality

\dfrac{a+b}{2} \geq \sqrt{ab}

Prove 1+\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+\dots+\dfrac{1}{n^2}<\dfrac{7}{4}

prove 1+\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+\dots+\dfrac{1}{n^2}<2

If \sqrt[3]{8x+6}=-3 , what is the value of x ?

For all x ≠ \dfrac{1}{2} , \dfrac{6x^2-x-2}{4x^2-1}=

Calculate the sum of the expression

2^x+2^x+2^x+2^x=

If a,b,c∈(0, ∞) and a+b+c=1 , prove 1/a+1/b+1/c≥9

Given positive numbers x , y , z , if xyz(x+y+z)=1 , find the minimum value of (x+y)(y+z) .

Given x＞0 , y＞0 and x ≠ y , compare the size of \dfrac{x^2}{y^2} +\dfrac{y^2}{x^2} and \dfrac{x}{y}+\dfrac{y}{x}