(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2008^2)(1-1/2009^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).……(1-1/2008)(1+1/2008)(1-1/2009)(1+1/2009)
=1/2 * 3/2 * 2/3 * 4/3 * 5/4……2007/2008 * 2008/2009 * 2010/2009
=1/2 * 2010/2009
=1005/2009
解：原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)···(1-1/2009)(1+1/2009)
=1/2·3/2·2/3·4/3·3/4·5/4···2008/2009·2010/2009
=1/2·2010/2009
=1005/2009
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