Pareto Distribution with parameters α and β: Prove that the variance does not exist if β≤2.

Question

A Pareto distribution with a pdf:

$f(x)=βα^β/x^(β+1), α<x<∞, α>0,β>0$

Note:$x$ to the power of $(β+1)$.

I estimated the mean and variance to be: $EX=αβ/(β-1)$, $Var X=(βα^2)/((β-2) (β-1)^2)$

What is the proof that if $β<2$, variance does not exist? I really would like to understand this point.

Thank you very much in advance for your help!