Induction for $3^n\geq n^2$ I need to prove by induction that $3^n\geq n^2$
What I have so far:


*

*Basis: $n = 1 \rightarrow 3^1 \geq 1^2 \rightarrow 3 \geq 1$

*Condition: $3^n\geq n^2$

*Assumption: $3^{n+1}\geq (n+1)^2$

*Basis: $3^n\geq n^2$
$3^{n+1}\geq (n+1)^2 
= 3(3^n) \geq n^2+2n+1 $
That's where I got stuck. I have no idea how to continue from there. 

Hint: For $n\geq 2$ we have $3n^2-(n+1)^2=2n^2-2n-1=(n^2-2)+(n-1)^2\ge0$.
