广州立讯检测有限公司:(1+1/2)x(1-1/2)x(1+1/3)x(1-1/3)x..........x(1+1/9)x(1-1/9)=?
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写出简算过程。如答案满意,35点奖励。
(1+1/2)x(1-1/2)x(1+1/3)x(1-1/3)x..........x(1+1/9)x(1-1/9)
=3/2*1/2*4/3*2/3*..........*10/9*8/9
=(3/2*4/3*5/4*..........*9/8*10/9)*(1/2*2/3*3/4*..........*7/8*8/9)
=10/2*1/9
=5/9
(1+1/2)x(1-1/2)x(1+1/3)x(1-1/3)x..........x(1+1/9)x(1-1/9)
=(1+1/2)*(1+1/3)..........*(1+1/9)*
(1-1/2)*(1-1/3)..........*(1-1/9)
=(3/2*4/3*5/4*..........*9/8*10/9)*(1/2*2/3*3/4*..........*7/8*8/9)
=10/2*1/9
=5/9
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