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1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7

1/n(n+1)(n+2)(n+3) =1/(n^2+3n)(n^2+3n+2) =1/2[1/(n^2+3n)-1/(n^2+3n+2)] =1/2[1/n(n+3)-1/(n+1)(n+2)]...

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