something appears to be wrong in the question because 1/2n(n+1) is a fraction and number of lines cannot be in fraction.
If n points lie in a plane and no three are collinear, prove that there are 1/2n(n-1) lines joining these points. I'm not really sure where to even start with proving this. I'm supposed to use proof by induction. Any help would be great. Thanks.
It is . To prove that by induction is a pain.
The base case is trivial: there is no line segment.
Suppose it is true for , there are points and line segments.
If you add one more point, then how many new line segments are added?
See if you can get