We are learning about proofs. We drew lines between noncollinear points. Our table showed 2 points >> 1 line segment, 3 point >> 3 line segments, 4 points >> 6 line segments, 5 points >> 10 line seg, 6 points >> 15 line seg. etc.

Write an expression in terms of n for the number of line segments that can be drawn between n points.

Please help.

n(n-1)/2

To find the expression for the number of line segments that can be drawn between n points, we need to look for a pattern in the given table.

From the table, we can observe that when there are 2 points, we can draw 1 line segment. When there are 3 points, we can draw 3 line segments. When there are 4 points, we can draw 6 line segments. When there are 5 points, we can draw 10 line segments. And when there are 6 points, we can draw 15 line segments.

To find the pattern, let's consider the difference between consecutive terms in the number of line segments. In this case, the differences are 2, 3, 4, and 5. Notice that these differences form a sequence of consecutive positive integers.

Therefore, we can express the number of line segments in terms of n using the formula for the sum of consecutive positive integers. This formula is the arithmetic series formula:
Sn = (n/2)(a + l)

Where Sn is the sum of the first n terms, n is the number of terms, a is the first term, and l is the last term.

In this case, a is 1, and the last term can be calculated by subtracting the previous term's difference from n.
So the formula becomes:

Sn = (n/2)(1 + (n-1))

Simplifying this expression, we get the formula for the number of line segments:

Sn = (n/2)(n)

Therefore, the expression in terms of n for the number of line segments that can be drawn between n points is (n/2)(n).