Prove $3^n \geq 2n^2 +1$ for $n = 1,2,\ldots$ using induction
This is what I have so far
Base case - $n=1,3^1 \geq 2^1 + 1 = 3$ true
Induction step - Assume true for some n, then,
$ 3*3^n \geq 3*(2n^2 +1)=6n^2 +3 $
I have to somehow manipulate and show its $\geq 2*(n+1)^2 +1$