(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+...+(-1/2007*1/2008)
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(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+...+(-1/2007*1/2008)(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+...+(-1/2007*1/200
(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+...+(-1/2007*1/2008)
(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+...+(-1/2007*1/2008)
(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+...+(-1/2007*1/2008)
(-1*2/1)+ (-2/1*3/1)+(-3/1*4/1)+...+(-2007/1*2008/1)
=(1/2-1)+(1/3-1/2)+(1/4-1/3)+……+(1/2008-1/2007)
=1/2-1+1/3-1/2+1/4-1/3+……+1/2008-1/2007
中间互相抵消
=-1+1/2008
=-2007/2008
是2007
2009
-1+1/2-1/2+1/3-1/3-1/4+1/4-...-1/2007+1/2008=-2007/2008
原式=-1+1/2-1/2+1/3-1/3+1/4-...+1/2007-1/2007+1/2008=-1+1/2008=-2007/2008。