原式= 2009×(1＋1／2＋1／3＋.＋1／2008）-2008×1-（2008-1）×1/2-(2008-2) ×1/3.-(2008-2007)×1/2008
=(2009-2008)×1+(2009-2008+1）×1/2+(2009-2008+2)×1/3.+(2009-2008+2007)×1/2008
=1+2×1/2+3×1/3.2008×1/2008
=1+1+1.+1
=2008
望LZ采纳@@!
2009*（1+1/2+1/3+……+1/2008）-[1+（1+1/2+)+(1+1/2+3/1）+……+1+1/2+
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