How can I prove that the sequence $f_n$ = \begin{cases} 0 & \text{,if $\vert x \vert \gt \frac{1}{n}$ } \\ n(1 + nx), & \text{,if $ \frac{1}{n}\le x \le 0$ } \\ n(1-nx) &\text{if $ 0\le x \lt \frac{1}{n} $} \end{cases}
converges pointwise ?
My attempt was using the archimedean property, i.e , for any $x$ I am able to find an $n^*$ such that $\vert x \vert \gt \frac{1}{n^*}$ and then we that $f_n(x) \rightarrow 0$ pointwise. Is that correct ? How can I use the definition to write this in a better way? Thanks ! ;)