it might be simple but I don't find a sequence $f_n: [0,1] \rightarrow \mathbb{R}, n \in \mathbb{N}$ that converges pointwise but not uniformly.
First I thought it could be $f_n(x) = \frac{x}{n}$ but it is not right, is it?
Thanks for help!
[Math] Sequence which converges pointwise but not uniformly
analysisconvergence-divergencereal-analysis
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Best Answer
$f_n(x)=x^n, x\in[0,1)$ $f_n(1)=1$
It converges pointwisely to $f(x)=0, x\in[0,1)$ $f(1)=1$ but not uniformly since uniformly convergence preserves continuity.
Your example converges uniformly on $[0,1]$.