Can you please help me with this question?

Question

A network with n points and a segment joining each point to every other point is called a complete network of size n. If k is the number of segments in a complete network of size n, which of the following is the number of segments in a complete network of size n + 1?

1. (A) k + n
2. (B) k + n + 1
3. (C) k + n + 2
4. (D) k + 2n + 1
5. (E) k + 2n + 2

Answer 1

n = 4, k = 6

n = 5, k = 9

n = 6, k = 12

n + 1 = k + 3

n + 1 = 2n + 2