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3/4*8/9*15/16*.*80/81*99/100
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3/4*8/9*15/16*.*80/81*99/100
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答案和解析
3/4*8/9*15/16*.*80/81*99/100
=(1-1/4)*(1-1/9)*(1-1/16)*...*(1-1/81)*(1-1/100)
=(1-1/2)(1+1/2)*(1-1/3)(1+1/3)*...*(1-1/9)(1+1/9)*(1-1/10)*(1+1/10)
=1/2*3/2*2/3*4/3*3/4*5/4*...*8/9*10/9*9/10*11/10
=1/2*11/10
=11/20
=(1-1/4)*(1-1/9)*(1-1/16)*...*(1-1/81)*(1-1/100)
=(1-1/2)(1+1/2)*(1-1/3)(1+1/3)*...*(1-1/9)(1+1/9)*(1-1/10)*(1+1/10)
=1/2*3/2*2/3*4/3*3/4*5/4*...*8/9*10/9*9/10*11/10
=1/2*11/10
=11/20
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