计算:(1+1/2)×(1-1/3)×(1+1/4)×(1-1/5)×.×(1+1/1000)×(1-1/1001)

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计算:(1+1/2)×(1-1/3)×(1+1/4)×(1-1/5)×.×(1+1/1000)×(1-1/1001)
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计算:(1+1/2)×(1-1/3)×(1+1/4)×(1-1/5)×.×(1+1/1000)×(1-1/1001)
计算:(1+1/2)×(1-1/3)×(1+1/4)×(1-1/5)×.×(1+1/1000)×(1-1/1001)

计算:(1+1/2)×(1-1/3)×(1+1/4)×(1-1/5)×.×(1+1/1000)×(1-1/1001)
1+1/2=3/2
1-1/3=2/3
(1+1/2)×(1-1/3)=1
(1+1/2n)×(1-1/(2n+1))=1
所以,
(1+1/2)×(1-1/3)×(1+1/4)×(1-1/5)×.×(1+1/1000)×(1-1/1001)=1

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