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

Perhaps you know that

and

Then the problem is trivial, since

Then

so that a = 3 and b = 1.

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i think the answer is true

step-by-step explanation: