# Is the function $\sum_{n=0}^{\infty} \frac{n^2x}{1+n^4x^2}$ continuous in $x \in (0, 1]$?

We know that the function $\sum_{n=0}^{\infty} \frac{n^2x}{1+n^4x^2}$ is convergent but not uniformly convergent when $x$ is in $(0, 1]$. How do we know if it's continuous or not, though?

Help much appreciated.

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Perhaps show it is uniformly convergent on $[a,1]$ for every $a>0$.
Continuous on a set means continuous at each point of the set. Given some point $u \in (0,1]$, show your sum is continuous at $u$. – GEdgar Nov 30 '11 at 4:36