The closed form sum of \(12 \left[ 1^2 \cdot 2 + 2^2 \cdot 3 + \ldots + n^2 (n+1) \right]\) for n ≥ 1 is n(n+1)(n+2)(an+b). Find an + b.

Presumably you mean find a and b (or, possibly, a + b).

I'm sure you can finish from here.

I am trying to find an + b, how would I do that?

Having found a and b (a = 3, b = 1) all you can do with an + b is to set it equal to 3n + 1.

The relationship is true for all n when a = 3 and b = 1.