Prove that $n + 2$ is odd where $n = 2k+1$ for some integer $k$

Prove that $n + 2$ is odd where $n = 2k+1$ for some integer $k$

I am attempting to learn about mathematical proofs on my own and this is
where I've started. I think I can prove this by induction. Something like:
$n = 2k+1$ is odd by definition
$n = 2k+1 + 2$ (this is where I'm stuck, how do I show that this is odd?)
$n = 2(k+1) + 1$ (if I can show that it's odd, I can do the same here and
prove my conjecture by induction, right?)
Thanks for any assistance