(1+1/2008+1/2009)*(1/2008+1/2009+1/2010)-(1+1/2008+1/2009+1/2010)*(1/2008+1/2009)
题目
(1+1/2008+1/2009)*(1/2008+1/2009+1/2010)-(1+1/2008+1/2009+1/2010)*(1/2008+1/2009)
(1+1/2008+1/2009)*(1/2008+1/2009+1/2010)-(1+1/2008+1/2009+1/2010)*(1/2008+1/2009)
答案
设1/2008+1/2009=t(1+1/2008+1/2009)*(1/2008+1/2009+1/2010)-(1+1/2008+1/2009+1/2010)*(1/2008+1/2009)=(1+t)(t+1/2010)-t(1+t+1/2010)=t(1+t)+(1+t)/2010-t(1+t)-t/2010=(1+t-t)/2010=1/2010
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