(1-1/2方)(1-1/3方)(1-1/4方)····(1-1/2007方)(1-1/2008方)我笨

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(1-1/2方)(1-1/3方)(1-1/4方)····(1-1/2007方)(1-1/2008方)我笨

(1-1/2方)(1-1/3方)(1-1/4方)····(1-1/2007方)(1-1/2008方)我笨
(1-1/2方)(1-1/3方)(1-1/4方)····(1-1/2007方)(1-1/2008方)
我笨

(1-1/2方)(1-1/3方)(1-1/4方)····(1-1/2007方)(1-1/2008方)我笨
2009/4016
1- 1/n^2 =((n-1)(n+1))/n^2
(1-1/2^2 )(1-1/3^2 )……(1-1/〖2007〗^2 )(1-1/〖2008〗^2 )=(1*3)/2^2 * (2*4)/3^2 * (3*5)/4^2 ……(2006*2008)/〖2007〗^2 * (2007*2009)/〖2008〗^2 =1/2 * 2009/2008=2009/4016