计算:(1/2+1/3+...+1/2011)*(1+1/2+1/3+...+1/2010)-(1+1/2+1/3+..
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计算:(1/2+1/3+...+1/2011)*(1+1/2+1/3+...+1/2010)-(1+1/2+1/3+...+1/2011)*(1/2+1/3+...+1/2010)
![计算:(1/2+1/3+...+1/2011)*(1+1/2+1/3+...+1/2010)-(1+1/2+1/3+..](/uploads/image/z/7800231-39-1.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A%281%2F2%2B1%2F3%2B...%2B1%2F2011%29%2A%281%2B1%2F2%2B1%2F3%2B...%2B1%2F2010%29-%281%2B1%2F2%2B1%2F3%2B..)
设1/2+...1/2010为a,则有
(a+1/2011)*(1+a)-(1+a+1/2011)*a
=a方+2012a/2011+1/2011-a方-2012a/2011
=1/2011
(a+1/2011)*(1+a)-(1+a+1/2011)*a
=a方+2012a/2011+1/2011-a方-2012a/2011
=1/2011