It seems i have issues understanding how to show that certain function series converge. I have done most of the assignment without any issues, but there were two terms that made it very confusing.
$$h_n(x) : \mathbb{R} \to \mathbb{R}, h_n(x) = max\{0,n-n^2|n-\frac{1}{n}|\} $$
In this case it is hard on how to obtain pointwise and uniform convergence out of the $max$ operator. If there are any explanations on this it would be great.
The second one requires only uniform convergence on the interval $[-1,1]$. Though i am rusty on the series convergence criteria. I would require a refresher or a solution to this one as well.
$$\sum_{n=1}^\infty \frac{1}{(2n+1)(2n-1)}(1-x^2)^n $$
I am currently too rusty to solve these problems on my own. I appreciate all the help you can give me.