(1+1/2004+1/2006+1/2008)*(1/2004+1/2006+1/2008+1/2010)-(1+1/2004+1/2006+1/2008+1/2010)*(1/)
题目
(1+1/2004+1/2006+1/2008)*(1/2004+1/2006+1/2008+1/2010)-(1+1/2004+1/2006+1/2008+1/2010)*(1/)
(1+1/2004+1/2006+1/2008)*(1/2004+1/2006+1/2008+1/2010)-(1+1/2004+1/2006+1/2008+1/2010)*(1/2004+1/2006+1/2008)
求简算
答案
设1/2004+1/2006+1/2008=A
=(1+A)*(A+1/2010)-(1+A+1/2010)*A
=(1+A)*(A+1/2010)-(A+2011/2010)*A
=(A平方+2011/2010A+1/2010)-(2011/2010A+A平方)
=1/2010
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