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?

Let $B > 1$ be given. We will show that for any such $B$ we can choose an $N \in \mathbb{N}$ such that $S_N \geq B$. This will show that the sequence diverges to $\infty$. Given $B$ we can choose $N > \sqrt{B - 1}$. Since $B > 1$, $N$ is well defined. Now solving for $N$ gives us $S_N = N^2 + 1 > B$. Thus we can choose an $N$ that will make our sequence larger than any number larger than $1$. This tells us the sequence diverges to $\infty$
