1减去2的2次方分之1再乘以1减去3的2次方分之1.乘以1减去100次方分之1
问题描述：
1减去2的2次方分之1再乘以1减去3的2次方分之1.乘以1减去100次方分之1
答
结果=101/200,化简之后就只剩下1/2乘以101/100
答
(1-1/2^2)*(1-1/3^2)*.....*(1-1/100^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)*....*(1-1/100)(1+1/100)
=1/2*3/2*2/3*4/3*......*99/100*101/100
=1/2*101/100
=101/200
答
(1-1/2²)(1-1/3²)...(1-1/100²)=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/100)(1+1/100)=(1/2)(3/2)(2/3)(3/4)(4/3)(5/4)(4/5)...(100/99)(99/100)(101/100) 中间都约分约掉了=(1/2)(101/100)=101/200...