Real Analysis : uniform convergence of sequence

Question

I was working on a real-analysis problem, but I got stuck, so could anybody please help me with this question?

Give an example of a sequence of continuous functions $\{f_n\}_{n\in\mathbb{N}}$ on the interval $[0,1]$ such that $f_n(x)\xrightarrow[n\to\infty]{}0$ for all $x\in[0,1]$, but the supremum of $f_n(x)$ is $1$ for all $n\in\mathbb{N}$.

Answer 1

Idea: $f_n$ piecewise linear, $f_n(x)=0$ for $x\in[0,1-2/n]\cup\{1\}$, $f_n(1/n)=1$.