The series
$$\frac{2x}{1+x^{2}}+\frac{4x^{3}}{1+x^{4}}+\frac{8x^{7}}{1+x^{8}}+\dots$$
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is uniformly convergent for all $x$
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is convergent for all $x$, but the convergence is not uniform
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is convergent only for $|x| \leq \frac{1}{2}$, but the convergence is not uniform
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is uniformly convergent on $\left [ \frac{-1}{2}, \frac{1}{2} \right ]$
