求值:(1/2+1/3+……+1/2012)*(1+1/2+1/3+……+1/2011)-(1+1/2+1/3+……+1/2012)*(1/2+1/3+……

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求值:(1/2+1/3+……+1/2012)*(1+1/2+1/3+……+1/2011)-(1+1/2+1/3+……+1/2012)*(1/2+1/3+……
求值:(1/2+1/3+……+1/2012)*(1+1/2+1/3+……+1/2011)-(1+1/2+1/3+……+1/2012)*(1/2+1/3+……

求值:(1/2+1/3+……+1/2012)*(1+1/2+1/3+……+1/2011)-(1+1/2+1/3+……+1/2012)*(1/2+1/3+……
1、这道题要用“假设法”来做,
2、假设a=1/2+1/3+……+1/2012 ,b=1/2+1/3+…… +1/2011
原式=a×(1+b)-(1+a)×b
=a+ab-b-ab
=a-b
=1/2+1/3+……+1/2012 -1/2-1/3-…… -1/2011
=1/2012

设1/2+1/3+1/4+......+1/2011=t
原式=(t+1/2012)*(1+t)-(1+t+1/2012)*t
=t^2+t+t/2012+1/2012-t-t^2-1/2012t
=1/2012