(1+1/2008+1/2009)*(1/2008+1/2009+1/2010)-(1+1/2008+1/2009+1/2010)*(1/2008+1/2009)

问题描述:

(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)

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