计算 (1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/2000^2)(1-1/2001^2)(1-1/2002^2)
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(1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/2000^2)(1-1/2001^2)(1-1/2002^2)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)……(1+1/2000)(1-1/2000)(1+1/2001)(1-1/2001)(1+1/2002)((1-1/2002)
=3/2x4/3x5/4x……x2001/2000x2002/2001x2003/2002x1/2x2/3x3/4x……x1999/2000x2000/2001x2001/2002
=2003/2x1/2002
=2003/4004
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)……(1+1/2000)(1-1/2000)(1+1/2001)(1-1/2001)(1+1/2002)((1-1/2002)
=3/2x4/3x5/4x……x2001/2000x2002/2001x2003/2002x1/2x2/3x3/4x……x1999/2000x2000/2001x2001/2002
=2003/2x1/2002
=2003/4004
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