Question

find the sum "SN" :

I'll post it in a second

Answer 1

\[\sum_{k=1}^{infinity} \frac{ 4 }{ k(k+1)(k+3)(k+4) }\]

I used partial fractions decomposition.

and found that A=4/3
B=-4/6
C=4/6
D=-4/12

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but when I try to find the SN "x1+x2+...xn+... " there's no relation between them so I can cross two off to get the SN.