How to prove the limit of a sequence using "$\epsilon-N$" I think I have a proper understanding of the general procedure, but I'm having difficulty manipulating my inequality so that I can isolate $n$ by itself. Sadly I wasn't given many examples to model my answer on.

Prove that $\displaystyle\lim_{n\to\infty}\frac{n+1}{n^2+1}=0$

So I'm given $L=0$. I then look at the inequality
$$\left| \frac{n+1}{n^2+1}-0\right|<\epsilon$$
but I have no idea how to isolate $n$. The best I can come up with, which may be the right idea, is to use another function $f$ such that
$$\left|\frac{n+1}{n^2+1}\right|<f<\epsilon$$
and then work with that. But my idea of using $f=\lvert n+1\rvert$ seems to have me a bit stuck too.

Hint: Show that $0<\frac{n+1}{n^2+1}<\frac{1}{n-1}$.
