简便计算(1+2/5)*(1-2/5)*(1+2/7)*(1-2/7)*.*(1+2/2005)*(1-2/2005)
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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)](/uploads/image/z/7326530-26-0.jpg?t=%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%281%2B2%2F5%29%2A%281-2%2F5%29%2A%281%2B2%2F7%29%2A%281-2%2F7%29%2A.%2A%281%2B2%2F2005%29%2A%281-2%2F2005%29)
(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
=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