i vertex has no segment, 2 vertex have 1 segment , 3 vertex have 3 segments, 4 vertex have 6 segment , 5 vertex have 10 segments, how many segments are needed to connect 20 points?

Answer 1

Let V = the number of vertices and S be the number of line segments that can connect the points.
S = N*(N-1)/2

Why? becasue each of the N points has N-1 points to connect to, but you have to divide by two to avoid counting each segment twice.