Question

Suppose you mark n points on a circle, where n is a whole number greater than 1. The number of segments you can draw that connect these points is
.
How many segments can you draw if you mark 8 points on the circle?

Answer 1

" that connect these points is
."

Is there supposed to be something here? Or is it asking for the formula here?

Answer 2

We are able to derive the formula using a bit of induction, but I do not know whether they simply included it or not.

Answer 3

Okay, I have to assume you are not paying attention here, so....

Assumption: We do \not\ know the formula.
To find this, let's just make some simple cases and build upon it. When we have 0 points, we obviously have 0 lines. When we have one point, we still have 0 lines. When we have 2 points, we can create one line.

Answer 4

When we add a third point, we have two points that it can connect to. So, two more lines are formed for a total of three lines.

Similarly, for a fourth point, we may create three more lines, one to each other point. What we can start to see here is that, for each additional point we add, we add one less than the total number of points we have to the number of line
Recursively, we have:
number of lines (n points) = number of lines (n-1 points) + n - 1
There is a common difference between N(n-1) and N(n) is always n-1, so it is simply a series adding the next # in line.
We could say that it is the sum from i=0 to n-1 of i, which simplifies down:
sum from i=0 to n-1 of i = (n-1)n/2 <- Number of lines at n points

Thus, our formula is: (n-1)n / 2 for n points.