We want to count the number of nonoverlapping segments formed by n collinear points, where nonoverlapping means that the segments are only formed between consecutive points.
We will see that for n points, we will have n - 1 segments between them.
To find it, we can find the number of non-overlapping segments for different values of n.
if n = 2 we have two points, then there is only one segment.
if n = 3 we have 3 points, then we can make two segments, where the middle point forms part of the two segments.
if n = 4 we have 4 points, and in this case we can see that we have 3 segments.
(the image at the end represents this, where the blue dots are the points and the space between them represents the segments)
So we already can see the pattern here, for n points, we will have n - 1 segments between them.
If you want to learn more, you can read:
https://brainly.com/question/16200284
