I am trying to prove that the following sequence of functions does not converge uniformly on $0\leq x <1$
$f_n(x)=nx^n$
The problem is probably at x=0 but I'm not sure how to show this
2026-04-06 06:30:52.1775457052
Prove Uniform Convergence of Sequence of Functions Fails
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Hint: The problem is at the other end, near $x=1$. Consider evaluating $f_n(x)$ at $x=1-\frac1n$, and remember the limit $$\lim_{n\to\infty}\left(1-\frac1n\right)^n=e^{-1}.$$ Multiplying the whole thing by $n$ just makes it worse.