（1-2平方分之1）（1-3平方分之1）（1-4平方分之1）.(1-99平方分之1）（1-100平方分之1）.

(1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2007^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).(1-1/2007)(1+1/2007)
=1/2*3/2*2*3*4/3*3/4*5/4*.*2006/2007*2008/2007
=1/2*2008/2007
=1004/2007

(1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2007^2)(1-1/2008^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).(1-1/2007)(1+1/2007)((1-1/2008)(1+1/2008)
=1/2*3/2*2*3*4/3*3/4*5/4*.*2006/2007*2008/2007*2007/2008*2009/2008
=1/2*2009/2008
=2009/4016

(1-2平方分之1)(1-3平方分之1)(1-4平方分之1)•••（1-10平方分之1）
=(1+1/2)x(1-1/2)x(1+1/3)x(1-1/3)x(1+1/4)x(1-1/4)x……x(1+1/10)x(1-1/10)
=(3/2x4/3x5/4x……x11/10)x(1/2x2/3x3/4x……x9/10)
=11/2x1/10
=11/20

=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/10)(1+1/10)
=1/2 × 3/2×2/3 × 4/3×3/4 × …… 10/9×9/10 ×11/10
=1/2×11/10
=11/20

(1-1/2²)(1-1/3²)(1-1/4²).(1-1/2004²)(1-1/2005²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)...(1+1/2004)(1-1/2004)(1+1/2005)(1-1/2005)
=(3/2)(1/2)(4/3)(2/3)(5/4)(3/4)...(2005/2004)(2003/2004)(2006/2005)(2004/2005)
=[(3/2)(4/3)(5/4)...(2006/2005)]×[(1/2)(2/3)(3/4)...(2004/2005)]
=[(3×4×5×...×2006)/(2×3×4×...×2005)]×[(1×2×3×...×2004)/(2×3×4×..×2005)]
=(2006/2)×(1/2005)
=1003/2005

1-2平方分之一 乘以 1-3^分之一乘以.1-2007^分之一=（1-1/2）×（1+1/2）×（1-1/3）×（1+1/3）×……×（1-1/2007）×（1+1/2007）=1/2×3/2×2/3×4/3×……×2006/2007×2008/2007中间可以约掉=1/2×2008/2007=1...

1=1