计算:6分之1+12分之1+20分之1+30分之1+42分之1等于

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计算:6分之1+12分之1+20分之1+30分之1+42分之1等于
计算:6分之1+12分之1+20分之1+30分之1+42分之1等于

计算:6分之1+12分之1+20分之1+30分之1+42分之1等于
1/6+1/12+1/20+1/30+1/42
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/2-1/7
=5/14

5/14

1/6+1/12+1/20+1/30+1/42
=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/2-1/7
=7/14-2/14
=5/14

1/6++1/12+1/20+1/30+1/42
=1/2×1/3+1/3×1/4+1/4×1/5+1/5×1/6+1/6×1/7
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/2-1/7
=5/14