Line split plane -- hangdian 2050

According to the line split plane, the intersection determines the number of rays and line segments, and then determines the number of new regions. When n-1 lines are broken, the number of areas is F (n-1 ). To maximize the number of added areas, the line segments on both sides of the line must be at the same time as the n-1 line edges, that is, 2 * (n-1) line segments. The number of new lines is 4 * (n-1) and the number of rays is 2. Note that only one area can be added to the adjacent two line segments. So: F (n) = f (n-1) + 4 (n-1) + 2-1 = f (n-1) + 4 (n-1) + 1 = f (n-2) + 4 (n-2) + 4 (n-1) + 2 ...... = F (1) + 4 + 4*2 + ...... + 4 (n-1) + (n-1) = 2n ^ 2-N + 1