Show that n lines separate the plane into (n^2 + n + 2) / 2 regions if no two of these lines are parallel and no three pass through a common point.
Okay, so I have to prove this by induction. I know this works for n =1 because if we have one line, it should divide into 2 regions (1^2 + 1 + 2) / 2 = 2 right? So since I have my base, I can assume that it is true for P(n) but my problem lies in showing that P(n+1) is true. All I know is that when we have the n+1 case, we know that the region is divided into n, with the additional line. I basically don't know what to do after this point. Any help is appreciated!