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1/(12*13)+1/(13*14)+1/(14*15)+1/(15*16)+1/(16*17)+1/(17*18)+1/(18*19)+1/(19*20)=?

分类: 作业答案 • 2021-12-28 14:33:56
问题描述：

1/(12*13)+1/(13*14)+1/(14*15)+1/(15*16)+1/(16*17)+1/(17*18)+1/(18*19)+1/(19*20)=?

答

1/a(a+1)=1/a-1/(a+1)1/(12*13)+1/(13*14)+1/(14*15)+1/(15*16)+1/(16*17)+1/(17*18)+1/(18*19)+1/(19*20)=1/12-1/13+1/13-1/14+1/14-1/15+……+1/19-1/12=1/12-1/20=5/60-3/60=2/60=1/15

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