Ok this hasn't been thought out well but I thought I would write down my initial thoughts.
For an n you have 1 set of (99 + 100) and 1 set of 101 on its own (I can't explian whats going on in my head for this part!).
The difference between the two is 98 so my guess is the change from to would happen at n=49.
Why I cant fully explain but something along the lines of that there's two things n acts on in on the LHS and one on the RHS and the RHS will 'catch' up to the LHS by 2 each time........
Ill think some more about what I'm actually trying to say but for now I think the change happens at n=49.