Does $f_n(x)=(\frac{2-x}{3})^n $ converge uniformly on $[-1,4]$?

Question

Does $f_n(x)=(\frac{2-x}{3})^n $ converge uniformly on $[-1,4]$?

I know that
$$f(x) = \begin{cases} \text{undefined} & x=-1 \\ 0 & x \in (-1,4] \end{cases}$$ and since $f(x)$ is discontinuous on$[-1,4 ]$, $f_n(x)$ does not converge uniformly on $[-1,4]$. Is it the correct answer?

Answer 1

Your pointwise limit should be,

$$ f(x) = \begin{cases}1 & \;\;\;\;x = -1\\ 0 & -1<x\leq 4 \end{cases} $$

But yes your argument holds otherwise.