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)?

i got f(n)=n^4=n^2/2+n^2/2+n/2

Answer 1

I got \[f(n)=\frac{n^{4}}{4} +n^{3}+n^{2} + n\]

Answer 2

\[T(n)=n ^{2}/2+n/2 =n(n+1)/2\]
\[T(n+1)=(n+1)((n+1)+1)/2=(n+1)(n+2)/2\]
\[f(n)=T(n)*T(n+1)=n(n+1)/2*(n+1)(n+2)/2\]
\[f(n)=n(n+1)^{2}(n+2)/4\]

Answer 3

n/2(n/2+1)(n+1)(n+2)