The question is clear in the title. I am trying to solve this recursion as a part of showing that the worst case of quicksort algorithm occurs when $k=0$, but can't do it. I could do the following specific cases (by repeatedly using the same recursion):
Can anybody please help me to solve this general case (or at least suggest some other way to prove that the worst case is $k=0$)?
P.S. I don't know Master's theorem, so I would appreciate a solution without using that (In case that is applicable here).