(1+2/5)*(1-2/5)*(1+2/7)*(1-2/7)*.*(1+2/2005)*(1-2/2005) 简便计算

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(1+2/5)*(1-2/5)*(1+2/7)*(1-2/7)*.*(1+2/2005)*(1-2/2005) 简便计算
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(1+2/5)*(1-2/5)*(1+2/7)*(1-2/7)*.*(1+2/2005)*(1-2/2005) 简便计算
(1+2/5)*(1-2/5)*(1+2/7)*(1-2/7)*.*(1+2/2005)*(1-2/2005) 简便计算

(1+2/5)*(1-2/5)*(1+2/7)*(1-2/7)*.*(1+2/2005)*(1-2/2005) 简便计算
=(1-2/5)(1+2/5)(1-2/7)(1+2/7)……(1-2/2005)(1+2/2005)
=3/5 × 7/5×5/7 × 9/7×7/9 ×…… × 2005/2003×2003/2005 ×2007/2005
=3/5×2007/2005
=6021/10025

(1+2/5)*(1-2/5)*(1+2/7)*(1-2/7)*.......*(1+2/2005)*(1-2/2005)
=7/5*3/5*9/7*5/7*...*2007/2005*2003/2005
=(7/5*9/7*...*2007/2005)*(3/5*5/7*...*2003/2005)
=2007/5*3/2005
=6021/10025

=(1-2/5)(1+2/5)(1-2/7)(1+2/7)……(1-2/2005)(1+2/2005)
=3/5 × 7/5×5/7 × 9/7×7/9 ×…… × 2005/2003×2003/2005 ×2007/2005
=3/5×2007/2005
=6021/10025