Prove that $f_n\to f$ uniformly does not imply $f_n^2 \to f^2$ uniformly.

Question

I've been searching for a function series $ f_n:[0,\infty] -> \mathbb{R} $ such that $ (f_n)_{n\geq1} $ uniformly converges to $f$, but $(f^2_n)_{n\geq1}$ does not uniformly converges to $f^2$.

I've tried it with many functions. Does anyone have a hint?

Answer 1

Hint: $$f_n(x) = x-\frac1n{}$$