Question

You have seen that the total number of lights in a triangular lighting rig is given by T(n) = n2/2 + n/2, while T(n+1) = n2/2 + 3n/2 + 1. If T(n) times T(n+1) = f(n), what is the reduced form of f(n)?

Answer 1

that is a convoluted way of asking you to simplify:
(n2/2 + n/2) (n2/2 + 3n/2 + 1)
can you multiply that out and collect the like terms?

Answer 2

f(n)=n^4/4+n^3+5n^2/4+n/2??
is this correct