1/1×2+1/3×4+1/4×5+……+1/2008×2009 1/1×3+1/3×5+……1/2007×2009 1
2个回答
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2008-1/2009)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2008-1/2009
中间正负抵消
=1-1/2009
=2008/2009
1/1×3+1/3×5+1/5×7 +……+1/2007×2009
=（1-1/3+1/3-1/5+1/5-1/7+……+1/2007-1/2009）/2
=（1-1/2009）/2
=1004/2009
1-2+3-4+5-6+……+2007-2008
=[1-2]+[3-4]+[5-6]+[7-8]+.+[2007-2008]
=[-1]+[-1]+.+[-1]
=-1*1004
=-1004
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