Question

please help me with #4

an recurrence relation for the number of regions determined by nonparallel lines such no three lines intersect at the same point. Show the steps, draw pictures. that

Answer 1

The recurrence relation, for n no of line i.e. if no two of the n lines are parallel then the necessary relation R is R_n = R_n - 1 + n supposes that you have n parallel linear then we should consider R_n only for n greaterthanorequalto k clearly R_k = k + L suppose that you have n linear for some n > k and you add a new line that is not parallel to any of the n existing lines. It will cross each of those lines. In order to cross n lines it must pass through n + 1 regions. If need each of those n regions in two so its adds n + 1 new regions. thus the recurrence is the same are in the case of no parallel lines R_n + 1 = R_n + n + 1 or R_n - R_n - 1 + n depending upon initial value.