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

Based on the scenario, the reduced form of f(n) is : 

f(n) = n^4/4+n^3 + 5n^2/4+n/2

or, it could also be written as

n/4 (n+1) (n^2 + 3n + 2)

hope this helps