初中计算题,难(1-1/2-1/3-……-1/2008)*(1/2+1/3+1/4+……+1/2009)-(1-1/2-
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初中计算题,难
(1-1/2-1/3-……-1/2008)*(1/2+1/3+1/4+……+1/2009)-(1-1/2-1/3-……-1/2009)*(1/2+1/3+1/4+……+1/2008)
(1-1/2-1/3-……-1/2008)*(1/2+1/3+1/4+……+1/2009)-(1-1/2-1/3-……-1/2009)*(1/2+1/3+1/4+……+1/2008)
(1-1/2-1/3-……-1/2008)*(1/2+1/3+1/4+……+1/2009)-(1-1/2-1/3-……-1/2009)*(1/2+1/3+1/4+……+1/2008)
=(1-1/2-1/3-……-1/2008)*(1/2+1/3+1/4+……+1/2009)-(1-1/2-1/3-……-1/2008)*(1/2+1/3+1/4+……+1/2008)+ 1/2009*(1/2+1/3+1/4+……+1/2008)
=(1-1/2-1/3-……-1/2008)*(1/2+1/3+1/4+……+1/2009 -1/2+1/3+1/4+……+1/2008)+1/2009*(1/2+1/3+1/4+……+1/2008)
=(1-1/2-1/3-……-1/2008)*1/2009+1/2009*(1/2+1/3+1/4+……+1/2008)
=(2-(1/2+1/3+1/4+……+1/2008))*1/2009+1/2009*(1/2+1/3+1/4+……+1/2008)
=2/2009 -(1/2+1/3+1/4+……+1/2008)*1/2009+1/2009*(1/2+1/3+1/4+……+1/2008)
=2/2009
=(1-1/2-1/3-……-1/2008)*(1/2+1/3+1/4+……+1/2009)-(1-1/2-1/3-……-1/2008)*(1/2+1/3+1/4+……+1/2008)+ 1/2009*(1/2+1/3+1/4+……+1/2008)
=(1-1/2-1/3-……-1/2008)*(1/2+1/3+1/4+……+1/2009 -1/2+1/3+1/4+……+1/2008)+1/2009*(1/2+1/3+1/4+……+1/2008)
=(1-1/2-1/3-……-1/2008)*1/2009+1/2009*(1/2+1/3+1/4+……+1/2008)
=(2-(1/2+1/3+1/4+……+1/2008))*1/2009+1/2009*(1/2+1/3+1/4+……+1/2008)
=2/2009 -(1/2+1/3+1/4+……+1/2008)*1/2009+1/2009*(1/2+1/3+1/4+……+1/2008)
=2/2009
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