I am to prove CS inequality by mathematical induction. Don't even know where to start. Any help?
Perhaps it's Cauchy-Schwartz?
The proof I usually use for Cauchy-Schwartz, in the form , is to consider the quadratic and observe that the requirement ("b^2-4ac") that f has at most one real root is precisely C-S. This doesn't depend on dimension.
If I had to do it by induction I think I'ld start by observing that it is trivial for n=1. The case n=2 follows from . The induction step would be something like , thus using the cases 2 and n-1.