I can't understand how to prove that
$ \sum\nolimits_{n=1}^{ \infty } u_n(x)$ converges uniformly at $[0,1]$, when $u_n(x) = (-1)^n*(1-x)*x^n$.
I tried using Weierstrass M-test - bounding those functions with a converging series $ \sum M_n$, which will result in $ |u_n(x)| \leq \sum M_n$. But after 1 and 1/2 hours I couldn't find the right usage here.
Would much appreciate help. Thank you!