I am working on some old analysis exams and i got stuck on this exercise : 

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> Using the epsilon definition show that $a\_{n} = n \cdot \left(\sqrt{1+ \frac{1}{n}} -1\right)$ converges and determine its limit.
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Knowing that the limit is 1/2, I know need to find an $ N \in \mathbb{N}$ so that : $ \forall \epsilon > 0 n > N \implies \left| a\_n - \frac{1}{2} \right| < \epsilon $

Next step I simplify $a\_n$ : $ a\_n = \frac{n \cdot \left(\sqrt{1+ \frac{1}{n}} -1\right) \cdot \sqrt{1+ \frac{1}{n}} + 1 } {\sqrt{1+ \frac{1}{n}} + 1} = \frac{1}{\sqrt{1+ \frac{1}{n}} + 1}$

And then I got stuck,what am I supposed to do with : $ \left|\frac{1}{\sqrt{1+ \frac{1}{n}} + 1} - \frac{1}{2} \right|$