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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 \(an + b.\)

 Apr 10, 2021
 #1
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an  + b is 4n - 1.

 Apr 10, 2021

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