要简便计算~(1/2-1)×(1/3-1)×(1/4-1)×(1/5-1)×(1/6-1)×(1/7-1)要简便计算

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要简便计算~(1/2-1)×(1/3-1)×(1/4-1)×(1/5-1)×(1/6-1)×(1/7-1)要简便计算
要简便计算~
(1/2-1)×(1/3-1)×(1/4-1)×(1/5-1)×(1/6-1)×(1/7-1)
要简便计算

要简便计算~(1/2-1)×(1/3-1)×(1/4-1)×(1/5-1)×(1/6-1)×(1/7-1)要简便计算
(1/2-1)×(1/3-1)×(1/4-1)×(1/5-1)×(1/6-1)×(1/7-1)
=(-1/2)×(-2/3)×(-3/4)×(-4/5)×(-5/6)×(-6/7)
约分
=1/7

= (-1)^6 1/2 2/3 3/4 4/5 5/6 6/7
=1/7

六个负数,最后结果是正数
原式=1/2×2/3×3/4×4/5×5/6×6/7=1/7 (约分)

(1/2-1)×(1/3-1)×(1/4-1)×(1/5-1)×(1/6-1)×(1/7-1)
=(1-1/2)×(1-1/3)×(1-1/4)×(1-1/5)×(1-1/6)×(1-1/7)
=1/2*2/3*3/4*4/5*5/6*6/7
=1/7

=(-1/2)×(-2/3)×(-3/4)×(-4/5)×(-5/6)×(-6/7)
=1/7

上述为
(1-2)/2*(1-3)/3*(1-4)/4*(1-5)/5*(1-6)/6*(1-7)/7
=(-1*-2*-3*-4*-5*-6)/(2*3*4*5*6*7)
=1/7

原式=(-1/2)×(-2/3)×(-3/4)×(-4/5)×(-5/6)×(-6/7) 分子分母也约去 又有6个数所以结果是正数 解得原式=1/7