计算(1/2-1)x(1/3-1)x(1/4-1)...(1/48-1)x(1/49-1)x(1/50-1)

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计算(1/2-1)x(1/3-1)x(1/4-1)...(1/48-1)x(1/49-1)x(1/50-1)计算(1/2-1)x(1/3-1)x(1/4-1)...(1/48-1)x(1/49-1)x

计算(1/2-1)x(1/3-1)x(1/4-1)...(1/48-1)x(1/49-1)x(1/50-1)
计算(1/2-1)x(1/3-1)x(1/4-1)...(1/48-1)x(1/49-1)x(1/50-1)

计算(1/2-1)x(1/3-1)x(1/4-1)...(1/48-1)x(1/49-1)x(1/50-1)
(1/2-1)x(1/3-1)x(1/4-1)...(1/48-1)x(1/49-1)x(1/50-1)
=-(1-1/2)(1-1/3)(1-1/4)*.*(1-1/48)(1-1/49)(1-1/50
=-1/2*2/3*3/4*4/5*...*47/48*48/49*49/50
=-1/50

1/2-1=1/2
1/3-1=2/3
1/4-1=3/4
...
1/49-1=48/49
1/50-1=49/50
因此原式即为
1/2 × 2/3 × 3/4 ....× 48/49 × 49/50
分子分母互相约去
最后得到
1/50

(1/2-1)x(1/3-1)x(1/4-1)...(1/48-1)x(1/49-1)x(1/50-1)
=(-1/2)x(-2/3)x(-3/4)...(-48/49)x(-49/50)
一共49个负号,所以相乘是负数
且前一个的分母和后一个的分子约分
=-1/50