When $(a-b)^n$, $n \geq 2$, $ab \neq 0$, is expanded by the binomial theorem, it is found that, when $a=kb$, where $k$ is a positive integer, the sum of the second and third terms is zero. The original answer is in the form of $mk+n$. Please find the value of $m+n$.

Let's think step by step and output the final answer within \boxed{}.
user