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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.

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    thank you for the advising!2011-12-10

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