Riesz-Fischer theorem

Let $\{e_n\}$ be an orthonormal basis for a (real or complex) infinite-dimensional Hilbert space $\mathscr{H}$. If $\{c_n\}$ is a sequence of (real or complex) numbers such that $\sum |c_n{|}^2$ converges, then there is an $x\in \mathscr{H}$ such that $x={\sum }_{n=1}^{\mathrm{\infty }}{c}_n{e}_n$, and $c_n=⟨x,e_n⟩$.