Can anyone help me solve part b for the following problem:
a) Find the recurrence relation satisfied by an, where an is the number of regions that a plane is divided into by n lines, if no two of the lines are parallel and no three of the lines go through the same point.
b) For the situation in part (a), let bn be the number of infinite regions that result. Find the recurrence relation for bn.
I found my recurrence relation for part a, but is bn the sum of all regions found in a) or what?
Thanks for any type of help you may provide me!