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?

$\forall\ N \in \mathbb{N}_{\ >\ 0}\,\,,\quad
n > \left\lfloor\,\sqrt{\,{N - 1}\,}\,\right\rfloor \implies n^{2} + 1 > N$.
