Sequence proof

**Mathman87** · May 10th 2010, 02:05 PM

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

**Plato** · May 10th 2010, 03:03 PM

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

**Mathman87** · May 10th 2010, 03:31 PM

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

Im having trouble with the general proof however?

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