Prove that the following function is continuous. I need to prove that the function:
$$f(x)=\tan{x}+\frac{\tan^2 x}{2^2}+\frac{\tan^3 x}{3^2}+\cdots+\frac{\tan^n x}{n^2}+\cdots$$
is continuous for $x \in \left[-\dfrac{\pi}{4}, \dfrac{\pi}{4} \right]$.
I don't really know where to begin. I see, that for $-\dfrac{\pi}{4}$ and $ \dfrac{\pi}{4}$ it is a sum of a certain series, but don't know how to show the continuity.

The sequence of partial sums is a uniformly convergent (hint: $\|\tan\|_{\infty} =1$) sequence of continuous functions. So its limit, $f$, must be continuous.
