初二数学（如果答的好，另有加分）

(1-1/2的平方)(1-1/3的平方)(1-1/4的平方)……(1-1/99的平方)(1-1/100的平方)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……（1-1/99)(1+1/99)(1-1/100)(1+1/100)
=(1/2)*(3/2)*(2/3)(4/3)(3/4)(5/4)……(98/99)(100/99)(99/100)(101/100)
=(1/2)*(101/100)
=101/200

[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+1/99][1-1/99][1+1/100][1-1/100]

=3/2*1/2*4/3*2/3.....100/99*98/99*101/100*99/100

=1/2*101/100

=101/200

用平方差解的
原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)......(1-1/99)(1+1/99)(1-1/100)(1+1/100)
=(1/2)[(3/2)(2/3)(4/3)(3/4)(5/4).....(98/99)(100/99)(99/100)](101/100)
=(1/2)*1*1*1....*1*(101/100)
=(1/2)(101/100)=101/200

原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)......(1-1/99)(1+1/99)(1-1/100)(1+1/100)
=(1/2)[(3/2)(2/3)(4/3)(3/4)(5/4).....(98/99)(100/99)(99/100)](101/100)
=(1/2)*1*1*1....*1*(101/100)
=(1/2)(101/100)=101/200
我是小学生，嘿嘿....