1/2加1/6加1/12加1/20加1/30加1/42加1/56等于?

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1/2加1/6加1/12加1/20加1/30加1/42加1/56等于?1/2加1/6加1/12加1/20加1/30加1/42加1/56等于?1/2加1/6加1/12加1/20加1/30加1/42加1/

1/2加1/6加1/12加1/20加1/30加1/42加1/56等于?
1/2加1/6加1/12加1/20加1/30加1/42加1/56等于?

1/2加1/6加1/12加1/20加1/30加1/42加1/56等于?
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+.1/6-1/7+1/7-1/8
=1-1/8
=7/8.

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

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

7/8