Are there references about universal power series and this statement?

Question

The notion of universal power series is linked with this statement :

We can find a power series $\sum_{n\ge1} a_nx^n$ such that for all continuous function $f : [0,1] \to \mathbb{R}$ such that $f(0)=0$ there exists a strictly increasing sequence of integers $(n_k)_{k\ge 0}$ such that the sequence $S_{n_k}(x)=\sum \limits_{n=1}^{n_k}a_nx^n$ is uniformly convergent to $f$.

So if anyone has references to dig this notion or this statement it would be great to share ! Is it a useful result ?

Thanks in advance !