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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 ≥ 1 is n(n+1)(n+2)(an+b). Find an + b.

 Mar 16, 2021
 #1
avatar+32410 
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Presumably you mean find a and b (or, possibly, a + b).

 

 

I'm sure you can finish from here. 

 Mar 16, 2021
 #2
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I am trying to find an + b, how would I do that?

Guest Mar 16, 2021
 #3
avatar+32410 
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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.

Alan  Mar 16, 2021

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