Show that $(n+1)^{n+1}>(n+2)^n$ for all positive integers Show that:
$(n+1)^{n+1}>(n+2)^n$  holds for all positive integers 
I tried using induction: 
for $n=1$ we have 4>3 then for $n+1$ we have to show that $(n+2)^{n+2}>(n+3)^{n+1}$ and here I stuck 

Since $(1+x)^n \geq 1 + nx, \forall x\geq -1$
$(\dfrac{n+1}{n+2})^n=(1-\dfrac{1}{n+2})^n \geq 1 -\dfrac{n}{n+2} = \dfrac{2}{n+2}$
$(n+1)\dfrac{2}{n+2} >1$
