Help, find a polynomial formula for d(n) in terms of n,give a geometric argument for formula to be true for n.

Let d(n) stand for the number of diagonals of a polygon of n sides. Here is a table of values of d(n).





n 3 4 5 6 7 8 9 10 11


d(n) 0 2 5 9 14 20 27 35 44Help, find a polynomial formula for d(n) in terms of n,give a geometric argument for formula to be true for n.
d(n) is a quadratic function, taking the form:





d(n) = (n^2 - 3n) / 2Help, find a polynomial formula for d(n) in terms of n,give a geometric argument for formula to be true for n.
d(n) = an虏 + bn + c


9a + 3b + c = 0


16a + 4b + c = 2


25a + 5b + c = 5


=%26gt; a = 0.5 ; b=-1.5; c=0


So we have


d(n) = (n虏 - 3n)/2, because the other values


give the right result


Geometric argument ? n(n-3), because a diagonal


can not end in the same corner and the two adjacent


corners and then divide by 2 because the diagonals


are counted double : from c1-%26gt;c2 =c2-%26gt;c1