# Thread: Sequence proof

1. ## Sequence proof

Can anyone give an $\epsilon$ - N proof that the sequence:

xn = ${\frac {2\,{n}^{2}+3}{4\,{n}^{2}+1}}$

tends to 1/2?

Also more generally, give the $\epsilon$ - N proof that the sequence {xn} n=1... infinity tends to x

2. If $0 < \varepsilon < 1$ let $n > \frac{{\sqrt {\frac{5}{{2\varepsilon }} - 1} }}{2}$.

3. Ok, i worked it through and i can understand that answer.

Im having trouble with the general proof however?