我不是他舅1/(1*4)+1/(4*7)+1/(7*10)+……+1/[(3n-2)(3n+1)]求和的

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我不是他舅1/(1*4)+1/(4*7)+1/(7*10)+……+1/[(3n-2)(3n+1)]求和的

我不是他舅1/(1*4)+1/(4*7)+1/(7*10)+……+1/[(3n-2)(3n+1)]求和的
我不是他舅
1/(1*4)+1/(4*7)+1/(7*10)+……+1/[(3n-2)(3n+1)]求和

我不是他舅1/(1*4)+1/(4*7)+1/(7*10)+……+1/[(3n-2)(3n+1)]求和的
1/[(3n-2)(3n+1)]=[1/(3n-2)-1/(3n+1)]*1/3
1/(1*4)+1/(4*7)+1/(7*10)+……+1/[(3n-2)(3n+1)]
=[(1/1-1/4)+(1/4-1/7)+(1/7-1/10)+...+(1/(3n-2)-1/(3n+1)]*1/3
=[1-1/(3n+1)]*1/3
=3n/(3n+1)*1/3
=n/(3n+1)