As stated in this question: A curve is contained in a hyperplane if and only if $\kappa_{n-1} = 0$
I'm learning differential geometry by myself and is now trying to prove that a curve of $\mathbb{R^n}$ is contained in a hyperplane if and only if $κ_{n−1}=0$, however I'm also not sure how to proceed.
There is a hint in the page 17 of this pdf, saying that "From above it is easy to see that a Frenet curve in $\mathbb{R^n}$ is contained in a hyperplane if and only if $κ_{n−1}\equiv 0$", but I cannot see why, can someone explain it to me, or just give me some hint?
https://www.math.cuhk.edu.hk/course_builder/1516/math4030/4030LectureNotesPart1.pdf