$f_n$ is defined on $[0,1] \ \ \forall n \in \mathbb{N} $,
$f_n(x)=\begin{cases} n(1-nx) &\mbox{if } \ 0 \leq x < \frac{1}{n} \\ 0 & \mbox{if } \ \frac{1}{n} \leq x \leq 1 \end{cases} $
The book says that show that $f_n$ converges to $f(x)=0 \ \forall x \in [0,1] $
But at $0, f_n(0)=n$ which does not converge. What am I doing wrong?