I hope this is the right subforum: the question stems from this other thread:

Induction of linear independent vectors

Use induction over to prove that for any field elements :

Ok, so there's nothing special about the formula.

i)

ii) but then... ?

I mean... what am I showing here, exactly, ?

Does this work?

I'm a bit confused about the inductive step in this kind of problem. It seems kind of obvious and I guess it's really just an example of the distributive law?