Originally Posted by

**rpatel** hi i didn't understand the following question

Let $\displaystyle \varepsilon>0$be given. For the following sequence $\displaystyle (a_{n})_{n\in\mathbb{N}}$find a natural number $\displaystyle N_{\varepsilon}$such that $\displaystyle \forall {\color{red}n}\geq N_{\varepsilon}$, $\displaystyle \vert a_{n}\vert<\varepsilon$thereby showing that $\displaystyle a_{n}\rightarrow0$as $\displaystyle n\rightarrow\infty$.

a) $\displaystyle a_{n}=\frac{n+\sqrt{n}}{n^{2}+1}$

thanks