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The closed form sum of 12[1^2*2+2^2*3+...+n^2(n+1)] for n>=1 is n(n+1)(n+2)(an+b). Find an+b.

 Aug 8, 2016
 #1
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"The closed form sum of 12[1^2*2+2^2*3+...+n^2(n+1)] for n>=1 is n(n+1)(n+2)(an+b). Find a and b."

 

sum

.

 Aug 8, 2016
 #2
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0

But what is n?

 Aug 8, 2016
 #3
avatar+33653 
0

n is an unspecified positive integer.  If you want a single numerical result for the sum you must specify the value for n.

 

For example:

 

n = 5    means  n(n+1)(n+2)(3n+1) = 3360

 

n=9     means   n(n+1)(n+2)(3n+1) = 27720

 

etc.

 

The sum is a function of n.

Alan  Aug 9, 2016

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