One line can split a surface to 2 part, 2 line can split a surface to 4 part. Given 100 lines, no two parallel lines, no three lines join at same point, how many parts can 100 line split? 5051 5053 5510 5511
直线数 平面个数
0 1
1 2
2 4
3 7
4 11
5 16
...
含有n条直线时，平面个数f(n) = f(n-1)+n
所以含有100条直线时，平面个数为f(99)+100 = f(98) + 99 + 100 = ... = f(0) + 1 +
2 + 3 + ... + 100 = 1 + 1 + 2 + 3 + ... + 100 = 5051
