Uniform convergence for $\sum_{n=1}^\infty n^\alpha x^{2n} (1-x)^2$ $$\sum_{n=1}^\infty n^\alpha x^{2n} (1-x)^2$$
a) Determine for every $\alpha$ where the series converges.
b) Show for every $\alpha$ if there is uniform convergence at $[-1,0]$ or $[0,1]$.
Can anybody help me out here a little bit ? How should I tackle this problem ?

Ok, Use Root Test.
$$ \lim_{n\rightarrow \infty} \sqrt[n]{n^{\alpha}x^{2n}(1-x)^2} $$
So, you get both answers from this. Does not depend on $\alpha$ but on $x$.
edit the absolute sign is missing.
