Let $$f_n(x)=\frac{x^2}{(1+x^2)^n}$$ be a sequence of functions from $[0,\infty)$ to $\mathbb{R}$.
Does the series of these functions converge uniformly on $[0,\infty)$?
What about $$f_n(x)=\frac{(-1)^{n-1}x^2}{(1+x^2)^n}$$
Thanks.
Let $$f_n(x)=\frac{x^2}{(1+x^2)^n}$$ be a sequence of functions from $[0,\infty)$ to $\mathbb{R}$.
Does the series of these functions converge uniformly on $[0,\infty)$?
What about $$f_n(x)=\frac{(-1)^{n-1}x^2}{(1+x^2)^n}$$
Thanks.