1/2+1/6+1/12+1/20+1/30+1/42+1/56=?

来源：百度知道编辑：UC知道时间：2024/05/30 15:18:14

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1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6/7+1/7*8
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8

原式=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7/8
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8

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1/2+1/6+1/12+1/20+1/30+1/42+1/56

=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(7*8)

=1-1/2+1/2-1/3+1/3-1/4+...+1/7-1/8

=1-1/8

=7/8

解：

原式=(1-/2)+(1/2-1/3)+(1/3-1/4)+……+(1/7-1/8)
=1-1/8
=7/8