How should I find the set, on which $f_n(x)=nx(1-x)^n$ converges pointwise and to find the limit function.
As for me I observe that $f_n(0)=0$ and $f_n(1)=0$ for all natural numbers $n$. So for all $x \in (0,1)$ the limiting function is $0$ as $n$ becomes a very big number! Am I correct?
For which values of x does $f_n(x)=nx(1-x)^n$ converge point-wise?
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real-analysis