Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1,
2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a
- b) = ab.

Trig Rules OK

Age 16 to 18 Challenge Level:

The problem suggests a property shared by the triangles which
always holds no matter how the squares are changed. The challenge
is to make and prove a conjecture about this property.