show sequence $n^2+1$ diverges 
Question: Show $S_n = n^2+1$ diverges.

My understanding of this question is proof by contradiction.
We first assume that $n^2+1$ converges to $s$. This implies that fix $\epsilon >0$, there exists $N$ s.t. $|n^2+1-s|< \epsilon$. I'm stuck here. anyhelp?

Hint: show that for any natural number $N$ there is some $k$ such that $S_{n} > N$ for all $n > k$.
