understanding notation of convergence in hilbert space

Question

In Dirk Werner's Functional Analysis, you can find this statement (Theorem V.4.9)

Let $H$ be a Hilbert space with ONB $S$. Since $S$ is an ONB, we can write $$ f=\sum_{e\in S}(f,e)_{H}e\quad\forall f\in H. $$ Can someone explain in one or two sentences what kind of convergence this is? I've read about so many types of convergence. The notation is quite confusing.

Answer 1

The convergence is in norm. That is, the partial sums of the right-hand side converge to $f$ in the norm on $H$.