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.$

Question

Mathematics

Kamden

10 January, 00:16

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.$

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Answers (1)

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Agustin Reilly · Answer 1

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.

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 $an +b.$

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.$