Is still true that if $\gamma: I \rightarrow \mathbb{R} ^n $ is a curve of class $C ^2$, and if $\tau (s)=0$, then $\gamma$ lies in a plane?

Question

I alredy make the proof when $n=3$ and i use the Frenet-Serret formulas, but i´m not sure how to do in $\mathbb{R} ^n$

Class of $C^2$ means twice continuously differentiable, and $\tau$ is the torsion of the curve.