12分之1+20分之1+30分之1+42分之1+56分之1的规律计算

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12分之1+20分之1+30分之1+42分之1+56分之1的规律计算

1/12+1/20+1/30+1/42+1/56
=1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/3-1/8
=5/24

1/12+1/20+1/30+1/42+1/56
=(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)
=1/3-1/8
=8/24-3/24
=5/24