Question

if n=1 in mathematical induction and its false do i keep on going with the k

Answer 1

That depends on the context. It could be that the statement applies "for all \(n>\) something", in which case the base case is \(n=\) something. Chances are \(n=1\) is the basis, so yes, if a given statement doesn't hold for \(n=1\) then the proof is finished.