(1-1/4)X(1-1/9)X(1-1/16).(1-1/10000)

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(1-1/4)X(1-1/9)X(1-1/16).(1-1/10000)
(1-1/4)X(1-1/9)X(1-1/16).(1-1/10000)

(1-1/4)X(1-1/9)X(1-1/16).(1-1/10000)
=(1-1/2^2)X(1-1/3^2)X(1-1/4^2).(1-1/100^2)
=[(2^2-1)/2^2]*[(3^2-1)/3^2]*[(4^2-1)/4^2].*[(100^2-1)/100^2]
利用平方差公式.分子分母写到一起
=3*1 *4*2*5*3.100*98 *101*99/(2^2*3^2*.100^2)
注意到分子中有3*4*5...101 和1*2*3.99与分母约就得到
=1*2*100*101/(2^2*100^2)=101/200

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