作业帮-1*1/2+(-1/2*1/3)+(-1/3*1/4)+···+(-1/2010*1/2011)
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-1*1/2+(-1/2*1/3)+(-1/3*1/4)+···+(-1/2010*1/2011)
-1*1/2+(-1/2*1/3)+(-1/3*1/4)+···+(-1/2010*1/2011)
-1*1/2+(-1/2*1/3)+(-1/3*1/4)+···+(-1/2010*1/2011)
原式=-（1-1/2)-(1/2-1/3)-(1/3-1/4)-········-(1/2010-1/2011) =-1+1/2-1/2+1/3-1/3+1/4-············-1/2010+1/2011 =-1+1/2011 =-2010/2011
记得采纳啊