用适当形式计算 (1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2007^2)(1-1/2008^2)
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用适当形式计算 (1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2007^2)(1-1/2008^2)
用适当形式计算 (1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2007^2)(1-1/2008^2)
用适当形式计算 (1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2007^2)(1-1/2008^2)
用平方差
原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/2008)(1+1/2008)
=(1/2)(3/2)(2/3)(4/3)……(2007/2008)(2009/2008)
=(1/2)(2009/2008)
=2009/4016
用适当形式计算 (1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2007^2)(1-1/2008^2)
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