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# The closed form sum of for is Find an+b.

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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.

May 29, 2020